Filtered ends of infinite covers and groups
Let f:A-->B be a covering map. We say A has e filtered ends with respect to f (or B) if for some filtration {K_n} of B by compact subsets, A - f^{-1}(K_n) "eventually" has e components. The main theorem states that if Y is a (suitable) free H-space, if K < H has infinite index, and i...
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Veröffentlicht in: | arXiv.org 2006-11 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | Let f:A-->B be a covering map. We say A has e filtered ends with respect to f (or B) if for some filtration {K_n} of B by compact subsets, A - f^{-1}(K_n) "eventually" has e components. The main theorem states that if Y is a (suitable) free H-space, if K < H has infinite index, and if Y has a positive finite number of filtered ends with respect to H\Y, then Y has one filtered end with respect to K\Y. This implies that if G is a finitely generated group and K < H < G are subgroups each having infinite index in the next, then 0 < {\tilde e}(G)(H) < \infty implies {\tilde e}(G)(K) = 1, where {\tilde e}(.)(.) is the number of filtered ends of a pair of groups in the sense of Kropholler and Roller. |
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ISSN: | 2331-8422 |