Homotopy colimits - comparison lemmas for combinatorial applications

Volkmar Welker, Gnter M. Ziegler, Rade T. Zivaljevic
1999 Journal für die Reine und Angewandte Mathematik  
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.
doi:10.1515/crll.1999.035 fatcat:sximrlw5abfxxgi3uw4b36m4oe