Lagrangian embeddings of the Klein bottle and combinatorial properties of mapping class groups

Vsevolod Shevchishin

Lagrangian embeddings of the Klein bottle and combinatorial properties of mapping class groups

Symplectic Geometry 2007-07-17 v1 Group Theory Geometric Topology

Authors: Vsevolod Shevchishin

Abstract

A proof of non-existence of Lagrangian embeddings of the Klein bottle K in \CP^2 is given. We exploit the existence of a special embedding of K in a symplectic Lefschetz pencil on \CP^2 and study its monodromy. As the main technical tool, we develop the theory of mapping class groups, considered as quotients of special Artin braid groups, and obtain some new results about combinatorial structure of such groups.

Keywords

lagrangian embedding klein bottle symplectic lefschetz pencil monodromy mapping class groups artin braid groups combinatorial structure

Cite

@article{arxiv.0707.2085,
  title  = {Lagrangian embeddings of the Klein bottle and combinatorial properties of mapping class groups},
  author = {Vsevolod Shevchishin},
  journal= {arXiv preprint arXiv:0707.2085},
  year   = {2007}
}

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50 pages, 3 figures

Lagrangian embeddings of the Klein bottle and combinatorial properties of mapping class groups

Abstract

Keywords

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