paper

A palindromization map for the free group

arXiv:0802.4359 · doi:10.1016/j.tcs.2008.09.011

Abstract

We define a self-map Pal: F_2 --> F_2 of the free group on two generators a, b, using automorphisms of F_2 that form a group isomorphic to the braid group B_3. The map Pal restricts to de Luca's right iterated palindromic closure on the submonoid generated by a, b, and is continuous for the profinite topology on F_2. The values of Pal are palindromes and coincide with the elements g of F_2 such that abg is conjugate to bag.

14 pages. Introduction expanded. Two references added. Sections 3 and 6 of Version 1 have been restructured, now forming Sections 3-4

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