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Moving basepoints and the induced automorphisms of link Floer homology

Sucharit Sarkar

Algebraic & Geometric Topology 15 (2015) 2479–2515
Abstract

Given an l–component pointed oriented link (L,p) in an oriented three-manifold Y , one can construct its link Floer chain complex CFL(Y,L,p) over the polynomial ring F2[U1,,Ul]. Moving the basepoint pi Li once around the link component Li induces an automorphism of CFL(Y,L,p). We study a (possibly different) automorphism of CFL(Y,L,p) defined explicitly in terms of holomorphic disks; for links in S3, we show that these two automorphisms are the same.

Keywords
link Floer homology, basepoint, mapping class group action, grid diagram
Mathematical Subject Classification 2010
Primary: 57M25
Secondary: 57M27, 57R58
References
Publication
Received: 18 September 2011
Revised: 25 June 2014
Accepted: 2 March 2015
Published: 10 December 2015
Authors
Sucharit Sarkar
Department of Mathematics
Princeton University
Fine Hall
Washington Rd
Princeton, NJ 08544
USA
http://web.math.princeton.edu/~sucharit/