The flow category of the action functional on ℒGN,N+K(ℂ)

David E. Hurtubise

doi:10.1215/ijm/1255984952

The flow category of the action functional on ℒG_N,N+K(ℂ)

David E. Hurtubise

Division of Mathematics & Natural Sciences (Altoona)

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

The flow category of a Morse-Bott-Smale function f_A: G_n(ℂ∞) → ℝ is shown to be related to the flow category of the action functional on the universal cover of ℒG_n,n+k(ℂ) via a group action. The Floer homotopy type and the associated cohomology ring of f_A: G_n(ℂ∞) → ℝ are computed. When n = 1 this cohomology ring is the Floer cohomology of G_1,1+k(ℂ).

Original language	English (US)
Pages (from-to)	33-50
Number of pages	18
Journal	Illinois Journal of Mathematics
Volume	44
Issue number	1
DOIs	https://doi.org/10.1215/ijm/1255984952
State	Published - 2000

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1215/ijm/1255984952

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abstract = "The flow category of a Morse-Bott-Smale function fA: Gn(ℂ∞) → ℝ is shown to be related to the flow category of the action functional on the universal cover of ℒGn,n+k(ℂ) via a group action. The Floer homotopy type and the associated cohomology ring of fA: Gn(ℂ∞) → ℝ are computed. When n = 1 this cohomology ring is the Floer cohomology of G1,1+k(ℂ).",

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AB - The flow category of a Morse-Bott-Smale function fA: Gn(ℂ∞) → ℝ is shown to be related to the flow category of the action functional on the universal cover of ℒGn,n+k(ℂ) via a group action. The Floer homotopy type and the associated cohomology ring of fA: Gn(ℂ∞) → ℝ are computed. When n = 1 this cohomology ring is the Floer cohomology of G1,1+k(ℂ).

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The flow category of the action functional on ℒG_N,N+K(ℂ)

Abstract

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