Involutory Hopf Group-coalgebras and Flat Bundles over 3-manifolds
نویسنده
چکیده
Given a group π, we use involutary Hopf π-coalgebras to define a scalar invariant of flat π-bundles over 3-manifolds. When π = 1, this invariant equals to the one of 3-manifolds constructed by Kuperberg from involutary Hopf algebras. We give examples which show that this invariant is not trivial.
منابع مشابه
The Equality of 3-manifold Invariants
The invariants of 3-manifolds defined by Kuperberg for involutory Hopf algebras and those defined by the authors for spherical Hopf algebras are the same for Hopf algebras on which they are both defined. Introduction The purpose of this paper is to compare two previously defined invariants of 3-manifolds. Let A be a finite-dimensional Hopf algebra over a field F with antipode S. Then if S = 1 t...
متن کاملInvolutory Hopf algebras and 3-manifold invariants
We establish a 3-manifold invariant for each finite-dimensional, involutory Hopf algebra. If the Hopf algebra is the group algebra of a group G, the invariant counts homomorphisms from the fundamental group of the manifold to G. The invariant can be viewed as a state model on a Heegaard diagram or a triangulation of the manifold. The computation of the invariant involves tensor products and con...
متن کاملLow dimensional flat manifolds with some classes of Finsler metric
Flat Riemannian manifolds are (up to isometry) quotient spaces of the Euclidean space R^n over a Bieberbach group and there are an exact classification of of them in 2 and 3 dimensions. In this paper, two classes of flat Finslerian manifolds are stuided and classified in dimensions 2 and 3.
متن کاملA Categorical Approach to Turaev’s Hopf Group-coalgebras
We show that Turaev’s group-coalgebras and Hopf group-coalgebras are coalgebras and Hopf algebras in a symmetric monoidal category, which we call the Turaev category. A similar result holds for group-algebras and Hopf group-algebras. As an application, we give an alternative approach to Virelizier’s version of the Fundamental Theorem for Hopf algebras. We introduce Yetter-Drinfeld modules over ...
متن کاملA Remark on the Douady Sequence for Non-primary Hopf Manifolds
1. Introduction. To determine cohomology groups of holomorphic vector bundles or more general coherent analytic sheaves on complex manifolds is very important in several complex variables and complex geometry. For example, Cartan-Serre's theorem B and Kodaira's vanishing theorem are fundamental respectively in the studies of two classes of complex manifolds: Stein manifolds and projective algeb...
متن کامل