Monopole Floer homology for rational homology 3-spheres

2008/09/30 by Kim A. Froyshov, Kim A. Frøyshov · 49 citations
Mathematics · #Advanced Operator Algebra Research #Algebra over a field #Biology #Cellular homology #Floer homology #Gene #Genetics #Geometric and Algebraic Topology #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Khovanov homology #Magnetic monopole #Mathematics #Morse homology #Physics #Pure mathematics #Quantum mechanics #SPHERES #Symplectic geometry #math.DG #math.GT #msc:57R57 #msc:57R58

paper · pdf · doi:10.1215/00127094-2010-060

published in Duke Mathematical Journal 155(3) (Duke University Press) · 60 pages, to appear in Duke J. Math. v2: Minor improvements concerning orientations on pages 18-21. v3: Two new sections 4 and 14 have been added.

arxiv created 2010/04/02 · openalex publication_date 2010/11/16 · openalex created_date 2016/06/24 · arxiv updated 2019/12/19 · openalex updated_date 2026/08/05

Abstract

We give a new construction of monopole Floer homology for spin-c rational homology 3-spheres. As applications we define two invariants of certain smooth compact 4-manifolds with b₁=1 and b⁺=0.

Citations

• An instanton-invariant for 3-manifolds
• Holomorphic disks and topological invariants for closed three-manifolds

Cited by

• On the monopole Lefschetz number of finite-order diffeomorphisms
• The Seiberg–Witten equations on end‐periodic manifolds and an obstruction to positive scalar curvature metrics
• Floer homology [wikipedia]

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