2001/04/30 by Ciprian Manolescu · 54 citations
Mathematics · #Advanced Operator Algebra Research #CW complex #Finite type invariant #Floer homology #Geometric and Algebraic Topology #Homology (biology) #Homotopy #Homotopy and Cohomology in Algebraic Topology #Invariant (physics) #Relative homology #Transversality #math.DG #math.GT #msc:57R57 #msc:57R58
paper · pdf · doi:10.2140/gt.2003.7.889
published in Geometry & Topology 7(2), 889-932 (Mathematical Sciences Publishers) · v4, added errata: In Section 9, the Coulomb-Neumann condition should be replaced by a double Coulomb condition, as in Khandhawit's paper (arxiv:1401.7590). Other minor errors are fixed. The main results are unchanged. Version 3 was published in Geom. Topol. 7(2003) 889-932; current version contains appended errata. v5: added item (4) to the errata
openalex publication_date 2003/12/10 · openalex created_date 2016/06/24 · arxiv created 2019/06/24 · arxiv updated 2019/06/25 · openalex updated_date 2026/08/05
Using Furuta's idea of finite dimensional approximation in Seiberg-Witten theory, we refine Seiberg-Witten Floer homology to obtain an invariant of homology 3-spheres which lives in the S 1 -equivariant graded suspension category. In particular, this gives a construction of Seiberg-Witten Floer homology that avoids the delicate transversality problems in the standard approach. We also define a relative invariant of four-manifolds with boundary which generalizes the Bauer-Furuta stable homotopy invariant of closed four-manifolds.