S. K. Roushon
TIFR, Mumbai
June 3, 2025
How simple is a homotopy equivalence?: A homotopy equivalence between topological spaces is easy to define, however to see if two spaces are homotopy equivalent is a difficult task. We will start by giving examples of some concrete and intuitive homotopy equivalences between compact polyhedra or CW-complexes. Then will ask if an arbitrary homotopy equivalence is homotopic to the naturally occurring ones. We will describe a $K$-theoretic torsion which answers this question. Although a lot is known about this torsion, a complete picture is still an open problem.
TIFR, Mumbai
June 3, 2025
How simple is a homotopy equivalence?: A homotopy equivalence between topological spaces is easy to define, however to see if two spaces are homotopy equivalent is a difficult task. We will start by giving examples of some concrete and intuitive homotopy equivalences between compact polyhedra or CW-complexes. Then will ask if an arbitrary homotopy equivalence is homotopic to the naturally occurring ones. We will describe a $K$-theoretic torsion which answers this question. Although a lot is known about this torsion, a complete picture is still an open problem.