Fox pairings and generalized Dehn twists

Details Fox pairings and generalized Dehn twists Fox pairings and generalized Dehn twists

2011-09-24

arxiv.org/abs/1109.5248v2

Mathematics

Geometric Topology

39 pages, 3 figures. One reference added in this second version

Scientific paper

We introduce a notion of a Fox pairing in a group algebra and use Fox pairings to define automorphisms of the Malcev completions of groups. These automorphisms generalize to the algebraic setting the action of the Dehn twists in the group algebras of the fundamental groups of surfaces. This work is inspired by the Kawazumi-Kuno generalization of the Dehn twists to non-simple closed curves on surfaces.

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