ON A NOTION OF MAPS BETWEEN ORBIFOLDS II: HOMOTOPY AND CW-COMPLEX

WM Chen, University of Massachusetts - Amherst

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This is the pre-published version harvested from ArXiv. The published version is located at http://www.worldscinet.com/ccm/08/0806/S0219199706002283.html

Abstract

This is the second of a series of papers which is devoted to a comprehensive theory of maps between orbifolds. In this paper, we develop a basic machinery for studying homotopy classes of such maps. It contains two parts: (1) the construction of a set of algebraic invariants — the homotopy groups, and (2) an analog of CW-complex theory. As a corollary of this machinery, the classical Whitehead theorem (which asserts that a weak homotopy equivalence is a homotopy equivalence) is extended to the orbifold category.