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Journal of Topology Advance Access published online on October 28, 2007
Journal of Topology, doi:10.1112/jtopol/jtm009
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© 2007 London Mathematical Society

Artin groups and the fundamental groups of some moduli spaces

Eduard Looijenga

Faculteit Wiskunde en Informatica, University of Utrecht, P.O. Box 80.010, NL-3508 TA Utrecht, The Netherlands, looijeng{at}math.ruu.nl


  Abstract

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.

Received May 27, 2007.

2000 Mathematics Subject Classification 14J10, 20F36 (primary), 20F34, 14H10 (secondary)


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