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Homotopy colimits – comparison lemmas for combinatorial applications

Welker, Volkmar; Ziegler, Günter M.; Živaljević, Rade T.

We provide a “toolkit” of basic lemmas for the comparison of homotopy types of homotopy colimits of diagrams of spaces over small categories. We show how this toolkit can be used in quite different fields of applications. We demonstrate this with respect to 1. Björner's “Generalized Homotopy Complementation Formula” [5], 2. the topology of toric varieties, 3. the study of homotopy types of arrangements of subspaces, 4. the analysis of homotopy types of subgroup complexes.
Published in: Journal für die reine und angewandte Mathematik, 10.1515/crll.1999.509.117, De Gruyter
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  • This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.