Moving basepoints and the induced automorphisms of link Floer homology

Sarkar, Sucharit

doi:10.2140/agt.2015.15.2479

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Moving basepoints and the induced automorphisms of link Floer homology

Sucharit Sarkar

Algebraic & Geometric Topology 15 (2015) 2479–2515

DOI: 10.2140/agt.2015.15.2479

Abstract

Given an $l$ –component pointed oriented link $(L, p)$ in an oriented three-manifold $Y$ , one can construct its link Floer chain complex $C F L (Y, L, p)$ over the polynomial ring $F_{2} [U_{1}, \dots, U_{l}]$ . Moving the basepoint $p_{i} \in L_{i}$ once around the link component $L_{i}$ induces an automorphism of $C F L (Y, L, p)$ . We study a (possibly different) automorphism of $C F L (Y, L, p)$ defined explicitly in terms of holomorphic disks; for links in $S^{3}$ , 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/

Volume 15, issue 5 (2015)