Instanton Floer homology for lens spaces

Hirofumi Sasahira

doi:10.1007/s00209-012-1003-2

Instanton Floer homology for lens spaces

Hirofumi Sasahira

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

3 Citations (Scopus)

Abstract

Floer constructed instanton homology for integral homology three-spheres. In this paper, we extend instanton Floer homology to lens spaces L(p, q). Moreover we show a gluing formula for a variant of Donaldson invariant along lens spaces. As an application, we prove that X= ℂℙ²#ℂℙ² does not admit a decomposition X=X₁∪X₂. Here X₁ and X₂ are oriented, simply connected, non-spin four-manifolds with b⁺ = 1 and with boundary L(p, 2), and p is a prime number of the form 16N + 1.

Original language	English
Pages (from-to)	237-281
Number of pages	45
Journal	Mathematische Zeitschrift
Volume	273
Issue number	1-2
DOIs	https://doi.org/10.1007/s00209-012-1003-2
Publication status	Published - Feb 2013
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics(all)

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AB - Floer constructed instanton homology for integral homology three-spheres. In this paper, we extend instanton Floer homology to lens spaces L(p, q). Moreover we show a gluing formula for a variant of Donaldson invariant along lens spaces. As an application, we prove that X= ℂℙ2#ℂℙ2 does not admit a decomposition X=X1∪X2. Here X1 and X2 are oriented, simply connected, non-spin four-manifolds with b+ = 1 and with boundary L(p, 2), and p is a prime number of the form 16N + 1.

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