15 April 2016 The symplectic arc algebra is formal
Mohammed Abouzaid, Ivan Smith
Duke Math. J. 165(6): 985-1060 (15 April 2016). DOI: 10.1215/00127094-3449459

Abstract

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-algebra associated to the (k,k)-nilpotent slice Yk obtained by counting holomorphic discs which satisfy a suitable conormal condition at infinity in a partial compactification Y¯k. The space Y¯k is obtained as the Hilbert scheme of a partial compactification of the A2k1-Milnor fiber. 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.

Citation

Download Citation

Mohammed Abouzaid. Ivan Smith. "The symplectic arc algebra is formal." Duke Math. J. 165 (6) 985 - 1060, 15 April 2016. https://doi.org/10.1215/00127094-3449459

Information

Received: 6 January 2014; Revised: 16 June 2015; Published: 15 April 2016
First available in Project Euclid: 28 January 2016

zbMATH: 1346.53073
MathSciNet: MR3486414
Digital Object Identifier: 10.1215/00127094-3449459

Subjects:
Primary: 53D40
Secondary: 57M25

Keywords: Fukaya category , Khovanov homology , nilpotent slice , symplectic topology

Rights: Copyright © 2016 Duke University Press

Vol.165 • No. 6 • 15 April 2016
Back to Top