Finite subset spaces of closed surfaces
| dc.creator | Tuffley, Christopher | |
| dc.date | 2003-11-21 | |
| dc.date.accessioned | 2026-07-07T05:03:07Z | |
| dc.date.available | 2026-07-07T05:03:07Z | |
| dc.description | The kth finite subset space of a topological space X is the space exp_k X of non-empty finite subsets of X of size at most k, topologised as a quotient of X^k. The construction is a homotopy functor and may be regarded as a union of configuration spaces of distinct unordered points in X. We show that the finite subset spaces of a connected 2-complex admit "lexicographic cell structures" based on the lexicographic order on I^2 and use these to study the finite subset spaces of closed surfaces. We completely calculate the rational homology of the finite subset spaces of the two-sphere, and determine the top integral homology groups of exp_k Sigma for each k and closed surface Sigma. In addition, we use Mayer-Vietoris arguments and the ring structure of H^*(Sym^k Sigma) to calculate the integer cohomology groups of the third finite subset space of Sigma closed and orientable. | |
| dc.description | 40 pages, 5 .eps figures | |
| dc.identifier | https://arxiv.org/abs/math/0311371 | |
| dc.identifier | http://arxiv.org/abs/math/0311371 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69287 | |
| dc.subject | Geometric Topology | |
| dc.subject | 55R80 (54B20 55Q52) | |
| dc.title | Finite subset spaces of closed surfaces | |
| dc.type | text |