The symplectic arc algebra is formal
| Autor: | Ivan Smith, Mohammed Abouzaid |
|---|---|
| Přispěvatelé: | Apollo - University of Cambridge Repository |
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Khovanov homology
General Mathematics nilpotent slice 53D40 01 natural sciences Mathematics::Algebraic Topology Arc (geometry) Mathematics - Geometric Topology Mathematics::K-Theory and Homology Fukaya category 0103 physical sciences FOS: Mathematics 0101 mathematics Algebra over a field 53D40 57M25 Mathematics::Symplectic Geometry Mathematics Final version 010102 general mathematics Geometric Topology (math.GT) Mathematics::Geometric Topology Algebra symplectic topology Mathematics - Symplectic Geometry 57M25 Symplectic Geometry (math.SG) 010307 mathematical physics Symplectic geometry |
| Zdroj: | Duke Math. J. 165, no. 6 (2016), 985-1060 |
| Popis: | We prove a formality theorem for the Fukaya categories of the symplectic manifolds underlying symplectic Khovanov cohomology, over fields of characteristic zero. The key ingredient is the construction of a degree one Hochschild cohomology class on a Floer A-infinity algebra associated to the (k,k)-nilpotent slice Y, obtained by counting holomorphic discs which satisfy a suitable conormal condition at infinity in a partial compactification of Y. The partial compactification is obtained as the Hilbert scheme of a partial compactification of a Milnor fibre. A sequel to this paper will prove formality of the symplectic cup and cap bimodules, and infer that symplectic Khovanov cohomology and Khovanov cohomology have the same total rank over characteristic zero fields. Comment: 58 pages, 15 figures. Final version: minor corrections |
| Databáze: | OpenAIRE |
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