The generalized Dehn twist along a figure eight

Details The generalized Dehn twist along a figure eight The generalized Dehn twist along a figure eight

2011-04-12

arxiv.org/abs/1104.2107v2

Mathematics

Geometric Topology

22 pages, 6 figures, 2 tables; minor corrections and modifications have been done in v2

Scientific paper

For any unoriented loop on a compact connected oriented surface with one boundary component, the generalized Dehn twist along the loop is defined as an automorphism of the completed group ring of the fundamental group of the surface. If the loop is simple, this is the usual right handed Dehn twist, in particular realized as a mapping class of the surface. We investigate the case when the loop has a single transverse double point, and show that in this case the generalized Dehn twist is not realized as a mapping class.

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