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MSc Thesis Defense
Speaker: Bhavesh Padwal, CMI
Date: Tuesday, 16 April 2024
Time: 3:30-4.30 PM
Venue: Seminar Hall
A short introduction to the Hauptvermutung of geometric topology
Bhavesh Padwal
Chennai Mathematical Institute.
16-04-24

Abstract

Hauptvermutung (main conjecture) is an abbreviation for die Hauptvermutung der kombinatorischen Topologie (the main conjecture of combinatorial topology). The conjecture states that two homeomorphic PL manifolds are PL homeomorphic. The related Combinatorial Triangulation Conjecture states that every topological manifold admits a PL structure. Kirby and Siebenmann disproved this conjecture. In this talk, I will discuss the construction of triangulable topological manifolds that do not admit piecewise linear structure, providing a compelling counterexample to the Hauptvermutung. Additionally, I will also prove the existence of multiple PL structures on RP^n (n at least 5).