Mahan Mj

Papers

Most of these can be found on arxiv.org at this URL. Mathscinet reviews at this URL.



Geometric Group Theory, Kleinian Groups and Hyperbolic Geometry


  1. Cubulating Drilled bundles over graphs , with Biswajit Nag, arXiv:2310.16403

  2. Indiscrete common commensurators , with Jingyin Huang, arXiv:2310.04876

  3. Commensurated hyperbolic subgroups , with Nir Lazarovich and Alex Margolis, arXiv:2309.13644

  4. Greenberg-Shalom's commensurator hypothesis and applications , with Nic Brody, David Fisher, and Wouter van Limbeek, arXiv:2308.07785

  5. Matings, holomorphic correspondences, and a Bers slice , with Sabyasachi Mukherjee, arXiv:2304.12699

  6. Class number for pseudo-Anosovs , with Francois Dahmani, arXiv:2210.12824

  7. Mixing Properties of Stable Random Fields Indexed by Amenable and Hyperbolic Groups , with Parthanil Roy and Sourav Sarkar, arXiv:2205.15849

  8. Commensurators of normal subgroups of lattices, with D. Fisher and W. Van Limbeek, preprint, arXiv:2202.04027.

  9. Combining rational maps and Kleinian groups via orbit-equivalence , with Sabyasachi Mukherjee, Proceedings of the London Math. Soc., Volume 126, Issue 5, May 2023, Pages 1740-1809 arXiv:2103.00835

  10. Regluing graphs of free groups , with Pritam Ghosh, Algebraic and Geometric Topology, v. 22, no. 4, 1969-2006. , arXiv:2011.01256

  11. Propagating Quasiconvexity from Fibers , with Pranab Sardar, Israel J. Math. 247 (2022), pgs 923-953, arXiv:2009.11521

  12. Property (T) for Fiber Products, with Arghya Mondal, arXiv:2009.00279, Proc. Ind. Acad. Sc., Math. Sci. 132 (2022), no. 2, Paper No. 42

  13. First Passage Percolation on Hyperbolic groups, , with Riddhipratim Basu, arXiv:1909.03427, Advances in Math. 408 (2022), 108599

  14. Cubulating surface-by-free groups , with Jason Manning and Michah Sageev, preprint arXiv:1908.03545

  15. Commensurators of thin normal subgroups and abelian quotients, with Thomas Koberda, to appear in Algebraic and Geometric Topology 2023 arXiv:1907.04129.

  16. Surface group representations in SL(2,C) with finite mapping class orbits , (with Indranil Biswas, Subhojoy Gupta and Junho Peter Wang), Geometry and Topology 26 (2022), no. 2, pgs 679-719 .

  17. Monodromy representations of meromorphic projective structures , (with Subhojoy Gupta), Proc. Amer. Math. Soc. 148 (2020), no. 5, 2069-2078. arXiv:1905.10132.

  18. Meromorphic projective structures, grafting and the monodromy map, (with Subhojoy Gupta), Adv. Math. 383 (2021) 107673 arxiv:1904.03804.

  19. Tight trees and model geometries of surface bundles over graphs , Journal of the London Math. Society, Volume 102, Issue3, December 2020, Pages 1178-1222

  20. Commutators, commensurators, and PSL(2, Z) , arXiv:1810.11429 with Thomas Koberda, Journal of Topology, Volume14, Issue3, September 2021, Pages 861-876

  21. Discontinuous motions of limit sets , with Ken'ichi Ohshika, arXiv:1704.00269, Algebraic and Geometric Topology 21 (2021), no. 7, 3401-3444.

  22. Intersection properties of stable subgroups and bounded cohomology, with Yago Antolin, Alessandro Sisto and Samuel J. Taylor, arXiv:1612.07227, in Indiana Univ. Math. Journal, volume 68, issue 1, 2019 pp. 179-199.

  23. Horospheres in Degerate 3-manifolds , with Cyril Lecuire, arXiv:1606.07185, in Int. Math. Res. Not. IMRN, Volume 2018, Issue 3, 31 January 2018, Pages 816-861. This version incorporates an erratum

  24. Planes in Degerate 3-manifolds , arXiv:1604.01976, under revision.

  25. Height, Graded Relative Hyperbolicity and Quasiconvexity, with Francois Dahmani, arXiv:1602.00834, Journal d'Ecole Polytechnique, vol. 4 (2017) p. 515-556

  26. Algebraic Ending Laminations and Quasiconvexity, with Kasra Rafi, arXiv:1506.08036, Algebraic and Geometric Topology, 18-4 (2018), 1883--1916. DOI 10.2140/agt.2018.18.1883

  27. Controlled Floyd Separation and Non-relatively Hyperbolic Groups with Shubhabrata Das, , arXiv:1408.0879, J. Ramanujan Math. Soc. 30 (2015), no. 3, 267-294.

  28. Limits of limit sets III: The General Case,

  29. Limits of limit sets II: Geometrically Infinite Groups, (with Caroline Series), arXiv:1306.3081, Geometry and Topology, 21 (2017), no. 2, 647-692

  30. Limits of limit sets I, (with Caroline Series), arXiv:1107.0875 Geometriae Dedicata: Volume 167, Issue 1 (2013), Page 35-67

  31. Semiconjugacies Between Relatively Hyperbolic Boundaries, (with Shubhabrata Das), Groups, Geometry and Dynamics Volume 10, Issue 2, 2016, 733-752

  32. On Discreteness of Commensurators, arXiv:1006.5237 Geometry and Topology 15 (2011) 331-350

  33. Cannon-Thurston Maps for Kleinian Groups, arxiv:1002.0996, Forum of Mathematics Pi 5 (2017), e1, 49 pp.

  34. A Combination Theorem for Metric Bundles , arXiv:0912.2715 Geometric and Functional Analysis: Volume 22, Issue 6 (2012), Page 1636-1707 (with Pranab Sardar)

  35. Pattern Rigidity and the Hilbert-Smith Conjecture, arXiv:0906.4243, Geometry and Topology 16 (2012) 1205--1246,

  36. Splittings and C-Complexes, (with Peter Scott and G. A. Swarup), arXiv:0906.1149 Algebraic and Geometric Topology 9 (2009) 1971-1986

  37. Pattern Rigidity in Hyperbolic Spaces: Duality and PD Subgroups, (with Kingshook Biswas), Groups, Geometry and Dynamics, Volume 6, Issue 1, 2012, pp. 97-123

  38. Universal Cannon-Thurston Maps and Curve Complexes, (with Chris Leininger and Saul Schleimer), arXiv:0808.3521 Commentarii Mathematici Helevetici 86(4), 2011, pp. 769-816

  39. Relative Hyperbolicity, Trees of Spaces and Cannon-Thurston Maps, (with Abhijit Pal), arXiv:0708.3578 Geometriae Dedicata, 151(1), 2011, pp. 59-78,

  40. Mapping Class Groups and Interpolating Complexes: Rank, arXiv:0706.2740 J. Ramanujan Math. Soc. 24(4), 2009, pp. 341-357

  41. Relative Rigidity, Quasiconvexity and C-Complexes, arXiv:0704.1922, Algebraic and Geometric Topology 8 (2008) pp. 1691-1716

  42. Ending Laminations and Cannon-Thurston Maps, with an Appendix written jointly with Shubhabrata Das, arXiv:math/0701725, Geometric and Functional Analysis. Volume 24, Issue 1 (2014), Page 297-321

  43. A Combination Theorem for Strong Relative Hyperbolicity, (with Lawrence Reeves), arXiv:math/0611601 Geometry and Topology 12 (2008) pp. 1777-1798

  44. Cannon-Thurston Maps for Surface Groups, arXiv:math/0607509 Annals of Mathematics 179(1) 2014, p. 1--80

  45. Cannon-Thurston Maps for Surface Groups: An Exposition of Amalgamation Geometry and Split Geometry, arXiv:math/0512539 Geometry, Topology, and Dynamics in Negative Curvature, London Mathematical Society Lecture Note Series volume 425, 2016, p. 221-271

  46. Cannon-Thurston Maps, i-bounded Geometry and a theorem of McMullen, arXiv:math/0511104 Actes du seminaire Theorie spectrale et geometrie, vol 28, Annee 2009-10, 63-108; 2011

  47. Cannon-Thurston Maps for Pared Manifolds of Bounded Geometry, arXiv:math/0503581 Geometry and Topology 13 (2009) 189-245

  48. Cannon-Thurston Maps and Bounded Geometry, Teichmuller Theory and Moduli Problems No. 10, 2009, pp. 489-511, Proceedings of Workshop on Teichmuller Theory at HRI, Allahabad, published by Ramanujan Mathematical Society

  49. Height in splittings of hyperbolic groups Proc. Indian Acad. Sci. (Math. Sci.), Vol. 114, No. 1, February 2004, pp. 39-54

  50. On a Theorem of Scott and Swarup Proc. Amer. Math. Soc. 127(6), 1999, pp. 1625-1631

  51. Coarse extrinsic geometry: a survey Geometry & Topology Monographs 1 (1998), The Epstein Birthday Schrift, pp. 341-364, also available at this http URL

  52. Cannon-Thurston Maps for Trees of Hyperbolic Metric Spaces, J. Differential Geom. 48, 1998, pp. 135-164

  53. Ending Laminations for Hyperbolic Group Extensions Geom. Funct. Anal. vol.7 No. 2, 1997, pp. 379-402

  54. Cannon-Thurston Maps for Hyperbolic Group Extensions, Topology 37, 1998, pp. 527-538

  55. Maps on Boundaries of Hyperbolic Metric Spaces, PhD thesis, U.C. Berkeley, 1997

  56. Widths of Subgroups (with R. Gitik, E. Rips and M. Sageev), Transactions Amer. Math. Soc. 350 (1998) pp. 321-329

Probabilistic Geometry
  1. Mixing Properties of Stable Random Fields Indexed by Amenable and Hyperbolic Groups, , with Parthanil Roy and Sourav Sarkar, arXiv:2205.15849

  2. First Passage Percolation on Hyperbolic groups, , with Riddhipratim Basu, arXiv:1909.03427, Advances in Math. 408 (2022), 108599

  3. Stable Random Fields, Patterson-Sullivan measures and Extremal Cocycle Growth, (with Jayadev Athreya and Parthanil Roy), Probability Theory and Related Fields, 183 (2022), no. 3-4, pgs 681-714 2022

  4. Cheeger inequalities for graph limits, (with Abhishek Khetan), to appear in Annales de l'Institut Fourier, arxiv:1807.02225, 2022+

Surface group representations and Vector Bundles
  1. Surface group representations in SL(2,C) with finite mapping class orbits , (with Indranil Biswas, Subhojoy Gupta and Junho Peter Wang), Geometry and Topology 26 (2022), no. 2, pgs 679-719 arXiv:1707.00071.

  2. Monodromy representations of meromorphic projective structures , (with Subhojoy Gupta), Proc. Amer. Math. Soc. 148 (2020), no. 5, 2069-2078 arXiv:1905.10132.

  3. Meromorphic projective structures, grafting and the monodromy map, (with Subhojoy Gupta), Adv. Math. 383 (2021) 107673 arxiv:1904.03804.

  4. Stable Higgs bundles over positive principal elliptic fibrations, (with Indranil Biswas and Misha Verbitsky), Complex Manifolds 2018 vol. 5, p. 195-201 arxiv:1806.03838.

  5. Sasakian and Parabolic Higgs bundles, (with Indranil Biswas), Mathematical Physics, Analysis and Geometry, Volume 21 (2018), no. 1, 21:4.

  6. Representations of surface groups with finite mapping class group orbits, with Indranil Biswas, Thomas Koberda and Ramanujan Santharoubane, arXiv:1702.03622, Volume 24 (2018) 241-250, New York Journal of Mathematics.

  7. Higgs bundles on Sasakian manifolds, (with Indranil Biswas), arXiv:1607.073, International Mathematics Research Notices, Volume 2018, Issue 11, 1 June 2018, Pages 3490-3506, https://doi.org/10.1093/imrn/rnw329

Kaehler Groups and Topology of Algebraic Varieties
  1. One-relator Sasakian groups , (with Indranil Biswas), arXiv:2101.10835, Colloq. Math. 167 (2022), no. 1, pgs 159-170

  2. A splitting theorem for good complexifications , (with Indranil Biswas and A. J. Parameswaran), arXiv:1503.08006, Ann. Inst. Fourier (Grenoble) 66 (2016), no. 5, 1965-1985

  3. An almost complex Castelnuovo de Franchis theorem, (with Indranil Biswas), arXiv:1502.06205, Hokkaido Mathematical Journal Vol.47, No.1, February, 2018

  4. H_1-semistability for projective groups, (with Indranil Biswas), arXiv:1402.6418, Math. Proc. Cambridge Philos. Soc. 162 (2017), no. 1, 89-100.

  5. Quasiprojective three-manifold groups and complexification of three-manifolds, (with Indranil Biswas), arXiv:1403.2029, International Mathematics Research Notices, Vol. 2015, No. 20, pp. 10041-10068

  6. The Fujiki Class and Positive Degree Maps, (with Indranil Biswas and Gautam Bharali), arXiv:1312.5655 Complex Manifolds . Volume 2, Issue 1 (Jan 2015)

  7. Homotopical Height, , (with Indranil Biswas, Dishant Pancholi) arXiv:1302.0607, International Journal of Mathematics Vol. 25, No. 13 (2014) 1450123 (43 pages), DOI: 10.1142/S0129167X14501237

  8. Infinitesimal Deformations and Brauer Group of some generalized Calabi-Eckmann Manifolds, (with Indranil Biswas and Ajay Singh Thakur), Tokyo Journal of Mathematics Vol. 37, No. 1, 2014, pages 61-72.

  9. One-relator Kaehler Groups, arXiv:1201.5772 (with Indranil Biswas), Geometry and Topology 16 (2012) 2171-2186

  10. Three manifold groups, Kaehler groups and complex surfaces, (with Indranil Biswas, Harish Seshadri), arXiv:1101.1162, Communications in Contemporary Mathematics, 14, 1250038 (2012)


h-principle


  1. The Gromov-Tischler theorem for stratified spaces , with Balarka Sen arXiv:2205.10892, to appear in Rocky Mountain Journal of Mathematics

  2. h-principle for stratified spaces , with Balarka Sen to appear in International Math. Research Notices, 2023, arXiv:2205.10888

Miscellaneous
  1. Nash Equilibria via Duality and Homological Selection, (with Arnab Basu, Samik Basu), arXiv:1111.0754 Proceedings Indian Academy of Sciences (Math. Sci.), November 2014, Volume 124, Issue 4, pp 581-602

  2. Thurston boundary of Teichmuller spaces and the commensurability modular group (with Indranil Biswas and Subhashish Nag) Conformal Geometry and Dynamics 3, 1999, pp. 50-66

Expository
  1. The Sullivan dictionary and Bowen-Series maps, (with Sabyasachi Mukherjee) To appear in the 80th birthday volume of Dennis Sullivan, EMS surveys in Mathematical Sciences, edited by Basmajian, Koberda, Papadopoulos, Seade and Zeinalian. arxiv:2302.09827

  2. Combination Theorems in Groups, Geometry and Dynamics, (with Sabyasachi Mukherjee) In the tradition of Thurston II. Geometry and groups, 331--383, Springer, Cham, [2022], ©2022, edited by Ohshika and Papadopoulos. , arXiv:2103.10082

  3. Cannon-Thurston Maps, Proc. Int. Cong. of Math. 2018 Rio de Janeiro, Vol. 2 (pp. 903-936), arxiv:1712.00760

  4. Cannon-Thurston Maps in Kleinian groups and geometric group theory, Surveys in Differential Geometry, Vol. 25, No. 1 (2020), pp. 281-318,

  5. Models of ends of hyperbolic 3-Manifolds: A survey , Handbook of Teichmuller Theory, Vol 7, 2019, pp: 165-193 DOI: 10.4171/203-1/6

  6. Motions of limit sets: A survey , in Teichmuller Theory and Grothendieck-Teichmuller Theory, Editors: Lizhen Ji, Athanase Papadopoulos, Weixu Su, Higher Education Press, ISBN: 978-7-04-057638-2, July 2022.

  7. Geometrically finite and infinite Kleinian Groups , arXiv:1507.04165, Workshop on Dynamics, TIFR, April 2015.

  8. A Crash Course on Knots Workshop on Topology and Condensed Matter Physics, December 2015.

  9. A survey of low dimensional (Quasi)projective groups (with Indranil Biswas) Analytic and Algebraic Geometry, proceedings of conference at Hyderabad University, A. Aryasomayajula, I. Biswas, A. Morye, A.J. Parameswaran (eds.), Hindustan Book Agency, 2017, p. 49-65

  10. What is hyperbolic geometry? Asia Pac. Math. Newsl. 3 (2013), no. 1, 1-5.

Books
  1. Flexibility of group actions on the circle , with Sang-hyun Kim, Thomas Koberda, Volume 2231, Springer Lecture Notes in Mathematics, 2019

  2. Topology and Condensed Matter Physics. Proceedings of SERB-DST School: November-December, 2015. Edited by Somen Bhattacharjee, Mahan Mj and Abhijit Bandyopadhyay. TRiPS series, Hindusthan Book Agency, 2017

  3. Geometry, groups and dynamics. Proceedings of the ICTS Program: Groups, Geometry and Dynamics (GGD-2012) held at CEMS, Kumaun University, Almora, December 3-16, 2012. Edited by C. S. Aravinda, William M. Goldman, Krishnendu Gongopadhyay, Alexander Lubotzky, Mahan Mj and Anthony Weaver. Contemporary Mathematics, 639. American Mathematical Society, Providence, RI, 2015. xiii+369 pp. ISBN: 978-0-8218-9882-6

Slides
  1. Hyperbolic Geometry and Chaos on the Complex Plane

  2. Homotopical Height

  3. On Discreteness of Commensurators

  4. Pattern Rigidity

  5. Geometry and Dynamics of Kleinian Groups

  6. Shapes and Geometry of Surfaces

  7. What is hyperbolic geometry?