Academics

On pseudo-collarability and Z-compactifiablity of manifolds

Time:Tues., 16:00-17:00, Nov.28, 2023

Venue:Shuangqing Complex 双清综合楼, C654; Zoom ID: 405 416 0815, PW: 111111

Organizer:陈伟彦、高鸿灏、黄意、江怡 、林剑锋

Speaker:Shijie GU 谷世杰 Northeastern University

Abstract:

Siebenmann's landmark 1965 dissertation established conditions for compactifying open high-dimensional manifolds by adding boundaries, a process termed 'completion' or 'collaring'. Nearly six decades later, Gu-Guilbault broadened this scope to include noncompact manifolds with boundaries, offering a complete characterization of completable manifolds. However, the emergence of exotic universal covering spaces and shifts towards topics like the Borel and Novikov conjectures and geometric group theory, where fundamental groups at infinity are unstable, has necessitated extensions to the completion of manifolds. Key among these are pseudo-collarability, introduced by Guilbault in 2000, and Z-compactifiability, dating back to Anderson's 1967 work on infinite-dimensional manifolds. This talk aims to address the implication between these two concepts. Specifically, we will show that a well-established set of conditions proposed by Chapman and Siebenmann in 1976 assures Z-compactifiability of manifolds. Time permitting, we will also discuss some applications to the Borel conjecture.

DATENovember 28, 2023
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