ON A NOTION OF MAPS BETWEEN ORBIFOLDS II: HOMOTOPY AND CW-COMPLEX
This is the pre-published version harvested from ArXiv. The published version is located at http://www.worldscinet.com/ccm/08/0806/S0219199706002283.html
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.
WM Chen. "ON A NOTION OF MAPS BETWEEN ORBIFOLDS II: HOMOTOPY AND CW-COMPLEX" Communications in Contemporary Mathematics 8.6 (2006): 763-821.
Available at: http://works.bepress.com/weiminchen_chen/6