2016/05/10 by Francesco Lin · 8 citations
Mathematics · #Advanced Combinatorial Mathematics #Chain (unit) #Computation #Floer homology #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Magnetic monopole #Product (mathematics) #Spectral sequence #math.GT
paper · pdf · doi:10.1112/topo.12027
published in Journal of Topology 10(4), 921-969 (Wiley) · 43 pages, 14 figures. Comments very welcome!
arxiv created 2016/05/10 · openalex created_date 2016/06/24 · openalex publication_date 2017/09/13 · arxiv updated 2017/09/20 · openalex updated_date 2026/08/06
We study the behavior of Pin ( 2 ) -monopole Floer homology under connected sums. After constructing a (partially defined) A ∞ -module structure on the Pin ( 2 ) -monopole Floer chain complex of a three-manifold (in the spirit of Baldwin and Bloom's monopole category), we identify up to quasi-isomorphism the Floer chain complex of a connected sum with a version of the A ∞ -tensor product of the modules of the summands. There is a naturally associated spectral sequence converging to the Floer groups of the connected sum whose E 2 page is the Tor of the Floer groups of the summands. We discuss in detail a simple example, and use this computation to show that the Pin ( 2 ) -monopole Floer homology of S 3 has non-trivial Massey products.