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The equivalence of two Seiberg-Witten Floer homologies

Author: Tye Lidman; Ciprian Manolescu
Publisher: [Paris] : Société mathématique de France, 2018.
Series: Astérisque, 399.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
"We show that monopole Floer homology (as defined by Kronheimer and Mrowka) is isomorphic to the S¹-equivariant homology of the Seiberg-Witten Floer spectrum constructed by the second author"--Abstract.
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Document Type: Book
All Authors / Contributors: Tye Lidman; Ciprian Manolescu
ISBN: 9782856298831 2856298834
OCLC Number: 1045067572
Language Note: In English; abstracts in English and French.
Description: vii, 220 pages : illustrations ; 24 cm
Contents: Morse homology in finite dimensions --
The Seiberg-Witten Floer spectrum --
Monopole Floer homology --
Reduction to the Coulomb gauge --
Finite-dimensional approximations with tame perturbations --
Stationary points --
The approximate flow as a Morse equivariant quasi-gradient --
Gradings --
The Morse-Smale condition for the approximate flow --
Self-diffeomorphisms of configuration spaces --
Convergence of approximate trajectories --
Characterization of approximate trajectories --
The equivalence of the homology theories.
Series Title: Astérisque, 399.
Responsibility: Tye Lidman & Ciprian Manolescu.

Abstract:

"We show that monopole Floer homology (as defined by Kronheimer and Mrowka) is isomorphic to the S¹-equivariant homology of the Seiberg-Witten Floer spectrum constructed by the second author"--Abstract.

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