We give a construction of Turaev-Viro type (3+1)-TQFT out of a G-crossed braided spherical fusion category for G a finite group. The resulting invariant of 4-manifolds generalizes several known invariants in literature such as the Crane-Yetter invariant and Yetter's invariant from homotopy 2-types. Some concrete examples will be provided to show the calculations. If the category is concentrated only at the sector indexed by the trivial group element, a co-cycle in H^4(G,U(1)) can be introduced to produce another invariant, which reduces to the twisted Dijkgraaf-Witten theory in a special case. It can be shown that with a G-crossed braided spherical fusion category, one can construct a monoidal 2-category with certain extra structure, but th...
10 pagesTo every spherical tensor category (in the sense of Etingof, Douglas et al.) we define a fin...
10 pagesTo every spherical tensor category (in the sense of Etingof, Douglas et al.) we define a fin...
The aim of this work is to explain what a topological quantum field theory (TQFT) is and the relatio...
This thesis is devoted to the study of some quantum invariants of 3-manifolds and 4-manifolds as wel...
37 pages, 16 figuresInternational audienceWe introduce the notion of a relative spherical category. ...
37 pages, 16 figuresInternational audienceWe introduce the notion of a relative spherical category. ...
AbstractFor a group G, the notion of a ribbon G-category was introduced in Turaev (Homotopy field th...
37 pages, 16 figuresInternational audienceWe introduce the notion of a relative spherical category. ...
Abstract: Topological quantum field theories are invariants of manifolds which can be computed via c...
gives rise to the generalized Kashaev and Turaev-Viro-type 3-manifold invariants defined in [12] and...
It has been common wisdom among mathematicians that Extended Topological Field Theory in dimensions ...
This thesis contains various results on unitary 2-representations of finite groups and their 2-chara...
AbstractLet (V, Z) be a Topological Quantum Field Theory over a field f defined on a cobordism categ...
The study of topological quantum field theories increasingly relies upon concepts from higher-dimens...
10 pagesTo every spherical tensor category (in the sense of Etingof, Douglas et al.) we define a fin...
10 pagesTo every spherical tensor category (in the sense of Etingof, Douglas et al.) we define a fin...
10 pagesTo every spherical tensor category (in the sense of Etingof, Douglas et al.) we define a fin...
The aim of this work is to explain what a topological quantum field theory (TQFT) is and the relatio...
This thesis is devoted to the study of some quantum invariants of 3-manifolds and 4-manifolds as wel...
37 pages, 16 figuresInternational audienceWe introduce the notion of a relative spherical category. ...
37 pages, 16 figuresInternational audienceWe introduce the notion of a relative spherical category. ...
AbstractFor a group G, the notion of a ribbon G-category was introduced in Turaev (Homotopy field th...
37 pages, 16 figuresInternational audienceWe introduce the notion of a relative spherical category. ...
Abstract: Topological quantum field theories are invariants of manifolds which can be computed via c...
gives rise to the generalized Kashaev and Turaev-Viro-type 3-manifold invariants defined in [12] and...
It has been common wisdom among mathematicians that Extended Topological Field Theory in dimensions ...
This thesis contains various results on unitary 2-representations of finite groups and their 2-chara...
AbstractLet (V, Z) be a Topological Quantum Field Theory over a field f defined on a cobordism categ...
The study of topological quantum field theories increasingly relies upon concepts from higher-dimens...
10 pagesTo every spherical tensor category (in the sense of Etingof, Douglas et al.) we define a fin...
10 pagesTo every spherical tensor category (in the sense of Etingof, Douglas et al.) we define a fin...
10 pagesTo every spherical tensor category (in the sense of Etingof, Douglas et al.) we define a fin...
The aim of this work is to explain what a topological quantum field theory (TQFT) is and the relatio...