#### Volume 15, issue 5 (2015)

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 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1472-2739 ISSN (print): 1472-2747
Moving basepoints and the induced automorphisms of link Floer homology

### Sucharit Sarkar

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

Given an $l\phantom{\rule{0.3em}{0ex}}$–component pointed oriented link $\left(L,p\right)$ in an oriented three-manifold $Y$, one can construct its link Floer chain complex $CFL\left(Y,L,p\right)$ over the polynomial ring ${\mathbb{F}}_{2}\left[{U}_{1},\dots ,{U}_{l}\right]$. Moving the basepoint ${p}_{i}\in {L}_{i}$ once around the link component ${L}_{i}$ induces an automorphism of $CFL\left(Y,L,p\right)$. We study a (possibly different) automorphism of $CFL\left(Y,L,p\right)$ 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