Homotopy Types of Subspace Arrangements via Diagrams of Spaces.
Please always quote using this URN: urn:nbn:de:0297-zib-658
- We prove combinatorial formulas for the homotopy type of the union of the subspaces in an (affine, compactified affine, spherical or projective) subspace arrangement. From these formulas we derive results of Goresky & MacPherson on the homology of the arrangement and the cohomology of its complement. The union of an arrangement can be interpreted as the direct limit of a diagram of spaces over the intersection poset. A closely related space is obtained by taking the homotopy direct limit of this diagram. Our method consists in constructing a combinatorial model diagram over the same poset, whose homotopy limit can be compared to the original one by usual homotopy comparison results for diagrams of spaces.
| Author: | Günter M. Ziegler, R. T. Zivaljevic |
|---|---|
| Document Type: | ZIB-Report |
| Date of first Publication: | 1991/12/06 |
| Series (Serial Number): | ZIB-Report (SC-91-15) |
| ZIB-Reportnumber: | SC-91-15 |
| Published in: | Appeared in: Mathematische Annalen 295 (1993) pp. 527-574 |
