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Marked homeomorphisms and the realization problem

Published online by Cambridge University Press:  24 October 2008

Peter Greenberg
Peter Greenberg
Affiliation:
Université de Grenoble I, Institut Fourier, Laboratoire de Mathématiques, 38402 St Martin d'Hères Cedex (France)
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Extract

The role played by the classical braid groups in the interplay between geometry, algebra and topology (see [Ca]) derives, in part, from their definition as the fundamental groups of configuration spaces of points in the plane. Seeking to generalize these groups and to understand them better, one is led to ask: are there other discrete groups whose topological invariants arise from configuration spaces?

The groups of marked homeomorphisms (1·1) provide a positive response which is in some sense banal; the realization problem (1·5) is to find non-banal examples.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 119 , Issue 4 , May 1996 , pp. 575 - 596
Copyright
Copyright © Cambridge Philosophical Society 1996

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