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Pin(2)-equivariant Floer homology and homology cobordism

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Matthew Stoffregen (University of California, Los Angeles)
Friday 03 February 2017, 10:00-11:00
Seminar Room 1, Newton Institute.

If you have a question about this talk, please contact INI IT .

HTLW02 - 3-manifold workshop

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.