Fundamental Groups of Blow-ups
| dc.creator | Davis, M. | |
| dc.creator | Januszkiewicz, T. | |
| dc.creator | Scott, R. | |
| dc.date | 2002-03-13 | |
| dc.date | 2002-08-27 | |
| dc.date.accessioned | 2026-07-07T04:47:02Z | |
| dc.date.available | 2026-07-07T04:47:02Z | |
| dc.description | Many examples of nonpositively curved closed manifolds arise as blow-ups of projective hyperplane arrangements. If the hyperplane arrangement is associated to a finite reflection group W, and the blow-up locus is W-invariant, then the resulting manifold M will admit a cell decomposition whose maximal cells are all combinatorially isomorphic to a given convex polytope P. In other words, M admits a tiling with tile P. The universal covers of such examples yield tilings of R^n whose symmetry groups are generated by involutions but are not, in general, reflection groups. We begin a study of these ``mock reflection groups'', and develop a theory of tilings that includes the examples coming from blow-ups and that generalizes the corresponding theory of reflection tilings. We apply our general theory to classify the examples coming from blow-ups in the case where the tile P is either the permutohedron or the associahedron. | |
| dc.identifier | https://arxiv.org/abs/math/0203127 | |
| dc.identifier | http://arxiv.org/abs/math/0203127 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63557 | |
| dc.subject | Geometric Topology | |
| dc.title | Fundamental Groups of Blow-ups | |
| dc.type | text |