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Pin(2)-equivariant Floer homology and homology cobordism

Presented by: 
Matthew Stoffregen University of California, Los Angeles
Date: 
Friday 3rd February 2017 - 10:00 to 11:00
Venue: 
INI Seminar Room 1
Abstract: 
We review Manolescu's construction of the  -equivariant Seiberg-Witten Floer stable homotopy type, and apply it to the study of the 3-dimensional homology cobordism group. We introduce the `local equivalence' group, and construct a homomorphism from the homology cobordism group to the local equivalence group. We then apply Manolescu's Floer homotopy type to obstruct cobordisms between Seifert spaces. In particular, we show the existence of integral homology spheres not homology cobordant to any Seifert space. We also introduce connected Floer homology, an invariant of homology cobordism taking values in isomorphism classes of modules.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons