SGGTC this week

[Oleg Lazarev]

Dear all, 

There will not be a talk in the SGGTC seminar this week; the listed talk by Peter Lambert-Cole had to be cancelled. 

The Columbia Geometry and Topology seminar will have a talk by Kyle Hayden that may be of interest to people in the group. The talk will be at 2:00 pm in Room 520.  

Best, 

Oleg

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Kyle Hayden: Knots, spines, and exotic 4-manifolds

A "knot trace" is a simple 4-manifold obtained by attaching a thickened disk (i.e. a 2-handle) to the 4-ball along a knot in its boundary. These 4-manifolds arise in many contexts, including the construction of exotic smooth structures on 4-space. After a quick survey of this history, I'll use knot traces to present a simple alternative solution to a classical question about piecewise linear surfaces in 4-manifolds (Problem 4.25 on Kirby's list, recently resolved by Levine and Lidman). The underlying construction provides pairs of homeomorphic 4-manifolds X and X' such that X is a knot trace and yet X' is not diffeomorphic to any knot trace, including X. These "not knot traces" X' exhibit a variety of other curious phenomena; I'll briefly mention some applications to the study of handle decompositions of simply-connected 4-manifolds, Stein fillings of contact 3-manifolds, and knot concordance. This is joint work in progress with Lisa Piccirillo.

[Kh2970]

Haha dude no I said that McKee Krumpak’s talk is still on!!!!!

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[Oleg Lazarev]

Hi everyone, 

Actually, there will also be a talk in SGGTC at 1:00 pm in 407 by McKee Krumpak from Brandeis. We will meet at 11:30 in the lobby to go out for lunch. 

Best, Oleg

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McKee Krumpak: Twisted monopole h-invariants

I will describe a generalization of Froyshov’s h-invariant, defined for a pair (Y, A) where Y is an arbitrary closed 3-manifold and A is a subgroup H^1(Y, Z). This involves a calculation of the bar flavor of monopole Floer homology with coefficients in a local system associated to A. Time permitting, I will discuss a conjectural relationship with Mrowka-Ruberman-Saveliev’s Casson-type invariant of 4-manifolds with the homology of S^1×S^3.