Braid groups and Hodge theory
نویسندگان
چکیده
منابع مشابه
Braid groups and Hodge theory
This paper gives an account of the unitary representations of the braid group that arise via the Hodge theory of cyclic branched coverings of P, highlighting their connections with ergodic theory, complex reflection groups, moduli spaces of 1-forms and open problems in surface topology.
متن کاملDiscrete Morse Theory and Graph Braid Groups
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...
متن کاملOn the representation theory of braid groups
This work presents an approach towards the representation theory of the braid groups Bn. We focus on finite-dimensional representations over the field of Laurent series which can be obtained from representations of infinitesimal braids, with the help of Drinfeld associators. We set a dictionary between representation-theoretic properties of these two structures, and tools to describe the repres...
متن کاملOn Representations and K-theory of the Braid Groups
Let Γ be the fundamental group of the complement of a K(Γ, 1) hyperplane arrangement (such as Artin’s pure braid group) or more generally a homologically toroidal group as defined below. The subgroup of elements in the complex K-theory of BΓ which arises from complex unitary representations of Γ is shown to be trivial. In the case of real K-theory, this subgroup is an elementary abelian 2-group...
متن کاملEmbeddings of graph braid and surface groups in right-angled Artin groups and braid groups
We prove by explicit construction that graph braid groups and most surface groups can be embedded in a natural way in right-angled Artin groups, and we point out some consequences of these embedding results. We also show that every right-angled Artin group can be embedded in a pure surface braid group. On the other hand, by generalising to rightangled Artin groups a result of Lyndon for free gr...
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: Mathematische Annalen
سال: 2012
ISSN: 0025-5831,1432-1807
DOI: 10.1007/s00208-012-0804-2