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Marked homeomorphisms and the realization problem

Published online by Cambridge University Press:  24 October 2008

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

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
Copyright
Copyright © Cambridge Philosophical Society 1996

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