Frobenius Modules and Essential Surface Cobordisms∗
نویسندگان
چکیده
An algebraic system is proposed that represent surface cobordisms in thickened surfaces. Module and comodule structures over Frobenius algebras are used for representing essential curves. The proposed structure gives a unified algebraic view of states of categorified Jones polynomials in thickened surfaces and virtual knots. Constructions of such system are presented.
منابع مشابه
Open-closed strings: Two-dimensional extended TQFTs and Frobenius algebras
We study a special sort of 2-dimensional extended Topological Quantum Field Theories (TQFTs). These are defined on open-closed cobordisms by which we mean smooth compact oriented 2-manifolds with corners that have a particular global structure in order to model the smooth topology of open and closed string worldsheets. We show that the category of open-closed TQFTs is equivalent to the category...
متن کاملLink homology and Frobenius extensions
We explain how rank two Frobenius extensions of commutative rings lead to link homology theories and discuss relations between these theories, Bar-Natan theories, equivariant cohomology and the Rasmussen invariant. AMS Subject Classification: 57M27 Frobenius systems. Suppose ι : R −→ A is an inclusion of commutative rings, and ι(1) = 1. The restriction functor Res : A−mod −→ R−mod has left and ...
متن کامل2-dimensional Topological Quantum Field Theories and Frobenius Algebras
Category theory provides a more abstract and thus more general setting for considering the structure of mathematical objects. 2-dimensional quantum field theories arise in physics as objects that assign vector spaces to 1-manifolds and linear maps to 2-cobordisms. From a categorical perspective, we find that they are the same as commutative Frobenius algebras. Our main goal is to explain this e...
متن کاملRepresentations of the Homotopy Surface Category of a Simply Connected Space
At the heart of the axiomatic formulation of 1+1-dimensional topological field theory is the set of all surfaces with boundary assembled into a category. This category of surfaces has compact 1-manifolds as objects and smooth oriented cobordisms as morphisms. Taking disjoint unions gives a monoidal structure and a 1+1-dimensional topological field theory can be defined to be a monoidal functor ...
متن کاملFrobenius Properties and Maschke-type Theorems for Entwined Modules
Entwined modules arose from the coalgebra-Galois theory. They are a generalisation of unified Doi-Hopf modules. In this paper, Frobenius properties and Maschke-type theorems, known for Doi-Hopf modules are extended to the case of entwined modules.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009