Related papers: On mapping class groups and their TQFT representat…
This paper has 3 principal goals: (1) to survey what is know about mapping class and Torelli groups of simply connected compact Kaehler manifolds, (2) supplement these results, and (3) present a list of questions and open problems to…
A topological quantum field theory is introduced which reproduces the Seiberg-Witten invariants of four-manifolds. Dimensional reduction of this topological field theory leads to a new one in three dimensions. Its partition function yields…
In this paper we prove an identity in terms of generating functions which enables us to calculate the numbers of isomorphism classes of absolutely indecomposable semistable representations of quivers over finite fields.
This paper is a survey of the relationship between labelled configuration spaces, mapping class groups with marked points and function spaces. In particular, we collect calculations of the cohomology groups for the mapping class groups of…
We provide formulas for invariants defined on a tensor product of defining representations of unitary groups, under the action of the product group. This situation has a physical interpretation, as it is related to the quantum mechanical…
In this paper, we use a geometric technique developed by Gonz\'alez-Prieto, Logares, Mu\~noz, and Newstead to study the $G$-representation variety of surface groups $\mathfrak{X}_G(\Sigma_g)$ of arbitrary genus for $G$ being the group of…
There are many situations in geometry and group theory where it is natural, convenient or necessary to explore infinite groups via their actions on finite objects, i.e. via the finite quotients of the group. But how much understanding can…
We refine the construction of quasi-homomorphisms on mapping class groups. It is useful to know that there are unbounded quasi-homomorphisms which are bounded when restricted to particular subgroups since then one deduces that the mapping…
We consider a constructive modification of quantum-mechanical formalism. Replacement of a general unitary group by unitary representations of finite groups makes it possible to reproduce quantum formalism without loss of its empirical…
We explain that a bulk with arbitrary dimensions can be added to the space over which a quantum field theory is defined. This gives a TQFT such that its correlation functions in a slice are the same as those of the original quantum field…
The mapping class group of a surface with one boundary component admits numerous interesting representations including as a group of automorphisms of a free group and as a group of symplectic transformations. Insofar as the mapping class…
We study boundary conditions for extended topological quantum field theories (TQFTs) and their relation to topological anomalies. We introduce the notion of TQFTs with moduli level $m$, and describe extended anomalous theories as natural…
By recognizing them as fundamental groups of developable complexes of groups we prove that mapping class groups of compact orientable surfaces have finite asymptotic dimension.
This paper is a collection of lecture notes on the superfield approach in three- and four-dimensional supersymmetric quantum field theory. Many examples of the applications of this approach to different superfield models are considered.
We extend the Weil representation of infinite-dimensional symplectic group to a representation a certain category of linear relations.
Random matrix models have been extensively studied in mathematical physics and have proven useful in combinatorics. In this review paper we introduce a generalization of these models to a class of tensor models. As the topology and…
We define a new class of integrable vertex models associated to quantum groups at roots of unit
Homotopy Quantum Field Theories (HQFTs) were introduced by the second author to extend the ideas and methods of Topological Quantum Field Theories to closed $d$-manifolds endowed with extra structure in the form of homotopy classes of maps…
We construct a certain `cobordism category' ${\cal D}$ whose morphisms are suitably decorated cobordism classes between similarly decorated closed oriented 1-manifolds, and show that there is essentially a bijection between…
Group field theories represent a 2nd quantized reformulation of the loop quantum gravity state space and a completion of the spin foam formalism. States of the canonical theory, in the traditional continuum setting, have support on graphs…