The depth of a Riemann surface and of a right-angled Artin group

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2019-11-12 DOI:10.1007/s40062-019-00250-3

Yves Félix, Steve Halperin

引用次数: 2

Abstract

We consider two families of spaces, X: the closed orientable Riemann surfaces of genus \(g>0\) and the classifying spaces of right-angled Artin groups. In both cases we compare the depth of the fundamental group with the depth of an associated Lie algebra, L, that can be determined by the minimal Sullivan algebra. For these spaces we prove that

and give precise formulas for the depth.

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黎曼曲面和直角阿廷群的深度

我们考虑了两个空间族，X:属\(g>0\)的闭合可定向Riemann曲面和直角Artin群的分类空间。在这两种情况下，我们将基本群的深度与相关李代数L的深度进行比较，L可以由最小沙利文代数确定。对于这些空间，我们证明了这一点，并给出了精确的深度公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Homotopy and Related Structures Mathematics-Geometry and Topology

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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.