Pseudo-isotopies in 4-mfds

Time：Fri., 10:00-11:30 am, Nov. 7, 2025

Venue：Ningzhai (宁斋) 203

Organizer：G2T2 Group

Speaker：Xiayu Tan

G2T2 Seminar

Organizers：

G2T2 Group

Speaker：

Xiayu Tan 谈夏羽 (THU)

Time：

Fri., 10:00-11:30 am, Nov. 7, 2025

Venue：

Ningzhai (宁斋) 203

Title:

Pseudo-isotopies in 4-mfds

Abstract:

In this talk I'll first go through the definition of pseudo-isotopy and construct two obstructions discovered by Hatcher and Wagoner, for two diffeomorphisms being isotopic from being just pseudo-isotopic. When dim(X)>5 these two obstructions give a complete answer, but when dim(X)=5 there are only surjections while when dim(X)=4,this is neither surjective or injective. In this paper, Olivier Singh studied the image of both obstructions and proved a “stable surjection” in dim=4 case. Using the results, we can prove that for some 4-mfds X (S^2xS^1xI or (M_1#M_2)xI when M_i=K(\pi, 1)-space), we have infinitely many connected components in Diff(X,\partial X) which are pseudo-isotopic to id but not isotopic to id.

DATENovember 6, 2025

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