LdT Seminar - Thursday 21/11/2024 (Room 136)

[Rafael Torres]

Speaker: Valentina Bais (SISSA)

Title: On Dold-Whitney's parallelizability of 4-manifolds

Abstract: A smooth n-manifold is called parallizable if its tangent bundle is trivial.  We will sketch a "bare hands" proof of a well-known result due to Dold-Whitney, characterizing closed parallelizable 4-manifolds as those closed, orientable 4-manifolds having trivial Euler characteristic, first Pontryagin class and second Stiefel-Whitney class. In particular, we see how to recover this statement from an argument due to R. Kirby on the classification of principal SO(4)-bundles over the 4-sphere by means of their first Pontryagin class and Euler class. The aim of the talk is to convey a geometric interpretation of the above mentioned invariants, using handle decompositions of manifolds as the main tool.

Date: Thursday November 21st, 2024
Time: 11:00 am
Venue: Room 136