A homotopy double groupoid of a Hausdorff space
by
Klaus Heiner Kamps
FernUniversität Hagen, Germany
Coauthors: Ronald Brown (University of Wales Bangor, Great Britain), Keith A. Hardie (University of Cape Town, South Africa), Timothy Porter (University of Wales Bangor, Great Britain)

We associate to a Hausdorff space X a double groupoid, called the homotopy double groupoid of X. The construction is based on the geometric notion of thin square. Roughly speaking, a thin square is a continuous map from the unit square of the real plane into X which factors through a tree. More precisely, the homotopy double groupoid is a double groupoid with connection which, under the equivalence of categories between small 2-categories and double categories with connection given in [1], corresponds to the homotopy 2-groupoid of X constructed in [2].

References

1. R.Brown, G.H.Mosa, Double categories, 2-categories, thin structures and connections, Theory and Applications of Categories 5(1999), 163-175.
2. K.A.Hardie, K.H.Kamps, R.W.Kieboom, A homotopy 2-groupoid of a Hausdorff space, Applied Categorical Structures 8(2000), 209-234.

Date received: February 6, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafw-18.