Affine Artin groups and the fundamental groups of some moduli spaces

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We define for every affine Coxeter graph a certain factor group of the associated Artin group and prove that some of these groups appear as orbifold fundamental groups of moduli spaces. Examples are the moduli space of nonsingular cubic algebraic surfaces and the universal nonhyperelliptic smooth genus three curve. We use this to obtain a simple presentation of the mapping class group of a compact genus three topological surface with connected boundary. This leads to a modification of Wajnryb's presentation of the mapping class groups in the higher genus case that can be understood in algebro-geometric terms.
This is a substantial revision of the previous version with some of the proofs simplified and the exposition (we hope) improved. To keep the length reasonable (38 pages), the discussion of the hyperelliptic mapping class groups has been omitted

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Algebraic Geometry, Group Theory, 14J10 20F36 (Primary) 20F34 14H10 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/131416

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9801117
 http://arxiv.org/abs/math/9801117

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arXiv