Filtered ends of infinite covers and groups

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Filtered ends of infinite covers and groups

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作者：Tom Klein
刊名：Journal of Pure and Applied Algebra
出版年：2007
出版时间：February 2007
年：2007
卷：208
期：2
页码：727-732
全文大小：231 K

文摘

Let f:A→B be a covering map. We say that 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 1a137c9f414"" title=""Click to view the MathML source"">H-space, if K<H has infinite index, and if a1a668e53068b"" title=""Click to view the MathML source"">Y has a positive finite number of filtered ends with respect to HY, then Y has one filtered end with respect to KY. This implies that if G is a finitely generated group and K<H<G are subgroups each having infinite index in the next, then implies that , where is the number of filtered ends of a pair of groups in the sense of Kropholler and Roller.

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