Cohomology ring of tree braid groups and exterior face rings
نویسندگان
چکیده
For a tree T T and positive integer alttext="n"> n encoding="application/x-tex">n , let B Subscript n Baseline upper B encoding="application/x-tex">B_nT denote the -strand braid group on . We use discrete Morse theory techniques to show that cohomology ring H Superscript asterisk left-parenthesis T right-parenthesis"> H ? ( stretchy="false">) encoding="application/x-tex">H^*(B_nT) is encoded by an explicit abstract simplicial complex K K encoding="application/x-tex">K_nT measures -local interactions among essential vertices of that, in many cases (for instance when binary tree), exterior face determined
منابع مشابه
On the Cohomology Rings of Tree Braid Groups
Let Γ be a graph. The (unlabelled) 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. We use the methods and results of [10] to get a partial description of the cohomology rings H∗(BnT ), where T is a tree. Our results are then used to prove that BnT is a right-angled Artin group if and ...
متن کاملPresentations for the Cohomology Rings of Tree Braid Groups
If Γ is a finite graph and n is a natural number, then UCnΓ, the unlabelled configuration space of n points on Γ, is the space of all n-element subsets of Γ. The fundamental group of UCnΓ is the n-strand braid group of Γ, denoted BnΓ. We build on earlier work to compute presentations of the integral cohomology rings H∗(UCnT ;Z), where T is any tree and n is arbitrary. The results suggest that H...
متن کاملGraph Braid Groups Exterior Face Algebras and Differential Forms
I am a geometric group theorist. Geometric group theory is a highly interdisciplinary field focusing on the study of groups via their actions on geometric spaces. Geometric group theory uses the tools and approaches of algebraic topology, commutative algebra, semigroup theory, hyperbolic geometry, geometric analysis, combinatorics, computational group theory, computational complexity theory, lo...
متن کاملRing structures of mod p equivariant cohomology rings and ring homomorphisms between them
In this paper, we consider a class of connected oriented (with respect to Z/p) closed G-manifolds with a non-empty finite fixed point set, each of which is G-equivariantly formal, where G = Z/p and p is an odd prime. Using localization theorem and equivariant index, we give an explicit description of the mod p equivariant cohomology ring of such a G-manifold in terms of algebra. This makes ...
متن کاملRepresentations of Braid Groups via Determinantal Rings
We construct representations for braid groups Bn via actions of Bn on a determinantal ring, thus mirroring the setting of the classical representation theory for GLn. The representations that we construct fix a certain unitary form.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2022
ISSN: ['2330-0000']
DOI: https://doi.org/10.1090/btran/131