相对双曲对的相对上同调维数

IF 0.5 4区数学 Q2 MATHEMATICS

Journal of Homotopy and Related Structures Pub Date : 2026-02-26 DOI:10.1007/s40062-026-00403-1

Harsh Patil

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引用次数: 0

摘要

证明了相对双曲对（G， H）的相对上同维\(\textrm{cd}_R(G,H)\)在G不含r -扭转时总是有限的。我们也证明了在拟等距下这个维数是保留的，假设G是无扭转的，外围亚群H是无约束的，类型为\(F_{\infty }\)。作为我们方法的必然结果，我们在几种情况下计算\(\textrm{cd}_{\mathbb {Z}}(G,H)\)。

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Relative cohomological dimension of a relatively hyperbolic pair

We show that the relative cohomological dimension \(\textrm{cd}_R(G,H)\) of a relatively hyperbolic pair (G, H) is always finite when G does not contain R-torsion. We also show that this dimension is preserved under quasi-isometries, provided that G is torsion-free and the peripheral subgroup H is unconstricted and of type \(F_{\infty }\). As a corollary of our methods, we compute \(\textrm{cd}_{\mathbb {Z}}(G,H)\) in several cases.

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来源期刊

Journal of Homotopy and Related Structures MATHEMATICS-

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.