Compactifications of the homeomorphism group of a graph |
| |
Authors: | Atsushi Yamashita |
| |
Affiliation: | Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1, Komaba, Meguro-ku, Tokyo 153-8914, Japan |
| |
Abstract: | Let Γ be a countable locally finite graph and let H(Γ) and H+(Γ) denote the homeomorphism group of Γ with the compact-open topology and its identity component. These groups can be embedded into the space of all closed sets of Γ×Γ with the Fell topology, which is compact. Taking closure, we have natural compactifications and . In this paper, we completely determine the topological type of the pair and give a necessary and sufficient condition for this pair to be a (Q,s)-manifold. The pair is also considered for simple examples, and in particular, we find that has homotopy type of RP3. In this investigation we point out a certain inaccuracy in Sakai-Uehara's preceding results on for finite graphs Γ. |
| |
Keywords: | 57S05 54D35 57N20 58D05 54C60 |
本文献已被 ScienceDirect 等数据库收录! |
|