Floer homotopy theory, revisited

Authored by: Ralph L. Cohen

Handbook of Homotopy Theory

Print publication date:  December  2019
Online publication date:  December  2019

Print ISBN: 9780815369707
eBook ISBN: 9781351251624
Adobe ISBN:


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In three seminal papers in 1988 and 1989 A. Floer introduced Morse theoretic homological invariants that transformed the study of low dimensional topology and symplectic geometry. In [17] Floer defined an “instanton homology” theory for 3-manifolds that, when paired with Donaldson’s polynomial invariants of 4-manifolds defined a gauge theoretic 4-dimensional topological field theory that revolutionized the study of low dimensional topology and geometry. In [18], Floer defined an infinite dimensional Morse theoretic homological invariant for symplectic manifolds, now referred to as “Symplectic” or “Hamiltonian” Floer homology, that allowed him to prove a well-known conjecture of Arnold on the number of fixed points of a diffeomorphism ϕ 1 : M → ≅ M arising from a time-dependent Hamiltonian flow {ϕ t }0≤t≤1. In [16] Floer introduced “Lagrangian intersection Floer theory” for the study of interesections of Lagrangian submanifolds of a symplectic manifold.

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