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

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

2007-07-13

arxiv.org/abs/0707.2085v1

Mathematics

Symplectic Geometry

50 pages, 3 figures

Scientific paper

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.

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