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Journal of the London Mathematical Society 2003 68(2):493-510; doi:10.1112/S0024610703004381
© 2003 by London Mathematical Society
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© The London Mathematical Society

The l2-Cohomology of Artin Groups

M. W. Davis and I. J. Leary

Department of Mathematics, Ohio State University 231 W. 18th Avenue, Columbus, OH 43210, USA, mdavis{at}math.ohio-state.edu
Faculty of Mathematical Studies, University of Southampton Southampton, SO17 1BJ, i.j.leary{at}maths.soton.ac.uk

Received 21 February 2002. Revision received 28 October 2002.

For each Artin group, the reduced l2-cohomology of (the universal cover of) its ‘Salvetti complex’ is computed. This is a CW-complex which is conjectured to be a model for the classifying space of the Artin group. In the many cases when this conjecture is known to hold the calculation describes the reduced l2-cohomology of the Artin group.


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