1. The depth of a Riemann surface and of a right-angled Artin group
- Author
-
Yves Félix and Steve Halperin
- Subjects
Fundamental group ,Algebra and Number Theory ,Functional analysis ,Riemann surface ,010102 general mathematics ,Algebraic topology ,01 natural sciences ,Combinatorics ,55P62 ,symbols.namesake ,Number theory ,Genus (mathematics) ,0103 physical sciences ,Lie algebra ,FOS: Mathematics ,symbols ,Algebraic Topology (math.AT) ,Artin group ,Mathematics - Algebraic Topology ,010307 mathematical physics ,Geometry and Topology ,0101 mathematics ,Mathematics - 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 $$\begin{aligned} \text{ depth } \,{\mathbb {Q}}[\pi _1(X)] = \text{ depth }\, {L}\, \end{aligned}$$ and give precise formulas for the depth.
- Published
- 2019
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