Asymptotic homology of graph braid groups
نویسندگان
چکیده
We give explicit formulas for the asymptotic Betti numbers of unordered configuration spaces an arbitrary finite graph over field.
منابع مشابه
Presentations of Graph Braid Groups
Let Γ be a graph. The (unlabeled) configuration space UCnΓ of n points on Γ is the space of n-element subsets of Γ. The n-strand braid group of Γ, denoted BnΓ, is the fundamental group of UCnΓ. This paper extends the methods and results of [11]. Here we compute presentations for BnΓ, where n is an arbitrary natural number and Γ is an arbitrary finite connected graph. Particular attention is pai...
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If Γ is any finite graph, then the unlabelled configuration space of n points on Γ, denoted UCΓ, is the space of n-element subsets of Γ. The braid group of Γ on n strands is the fundamental group of UC Γ. We apply a discrete version of Morse theory to these UCΓ, for any n and any Γ, and provide a clear description of the critical cells in every case. As a result, we can calculate a presentation...
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Let (W, S) be a Coxeter system, with W a finite, irreducible Coxeter group and let GW be the associated Artin group (see Bourbaki [5] for an introduction to Coxeter groups and their classifications and Brieskorn and Saito [6] for relations between Coxeter groups and Artin groups ). The main objects of study of this paper are the Artin groups of type An . We recall that the Artin group GAn is th...
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ژورنال
عنوان ژورنال: Geometry & Topology
سال: 2022
ISSN: ['1364-0380', '1465-3060']
DOI: https://doi.org/10.2140/gt.2022.26.1745