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Floer theory and its topological applications

  • Takagi Lectures
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Japanese Journal of Mathematics Aims and scope

Abstract

We survey the different versions of Floer homology that can be associated to three-manifolds. We also discuss their applications, particularly to questions about surgery, homology cobordism, and four-manifolds with boundary. We then describe Floer stable homotopy types, the related Pin(2)-equivariant Seiberg–Witten Floer homology, and its application to the triangulation conjecture.

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  1. Department of Mathematics, UCLA, 520 Portola Plaza, Los Angeles, CA, 90095, USA

    Ciprian Manolescu

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Communicated by: Kaoru Ono

This article is based on the 14th Takagi Lectures that the author delivered at the University of Tokyo on November 15 and 16, 2014.

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Manolescu, C. Floer theory and its topological applications. Jpn. J. Math. 10, 105–133 (2015). https://doi.org/10.1007/s11537-015-1487-8

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