Balarka Sen
TIFR, Mumbai
August 24, 2023
h-principle for stratified spaces: Smale's sphere eversion paradox states that any two immersions of the 2-sphere inside the Euclidean 3-space are isotopic through immersions. This is an instance of a much more general phenomenon known as h-principles, introduced by Gromov, wherein sufficiently overdetermined partial differential relations occurring in geometry of manifolds can be solved by purely algebro-topological means. We shall discuss a generalization of h-principles in the setting of singular spaces, and prove as a corollary a version of the Smale-Hirsch theorem for positive-codimensional immersions between stratified spaces. The proof involves algebraic topology pertaining to certain Space-valued variants of constructible sheaves over stratified spaces that we call ``stratified continuous sheaves". Time permitting, I will mention parallels between our results and the main theorem of stratified Morse theory by Goresky and MacPherson. This is a joint work with Mahan Mj.
TIFR, Mumbai
August 24, 2023
h-principle for stratified spaces: Smale's sphere eversion paradox states that any two immersions of the 2-sphere inside the Euclidean 3-space are isotopic through immersions. This is an instance of a much more general phenomenon known as h-principles, introduced by Gromov, wherein sufficiently overdetermined partial differential relations occurring in geometry of manifolds can be solved by purely algebro-topological means. We shall discuss a generalization of h-principles in the setting of singular spaces, and prove as a corollary a version of the Smale-Hirsch theorem for positive-codimensional immersions between stratified spaces. The proof involves algebraic topology pertaining to certain Space-valued variants of constructible sheaves over stratified spaces that we call ``stratified continuous sheaves". Time permitting, I will mention parallels between our results and the main theorem of stratified Morse theory by Goresky and MacPherson. This is a joint work with Mahan Mj.