Instanton Floer homology for lens spaces

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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 languageEnglish
Pages (from-to)237-281
Number of pages45
JournalMathematische Zeitschrift
Volume273
Issue number1-2
DOIs
Publication statusPublished - Feb 2013
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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