We present a non-abelian generalization of Witten monopole equations and we analyze the associated moduli problem, which can be regarded as a generalization of Donaldson theory. The moduli space of solutions for SU(2) monopoles on Kähler manifolds is discussed. We also construct, using the Mathai-Quillen formalism, the topological quantum field theory corresponding to the new moduli problem. Th...

During the last decade, a lot of progress has been made in the enumerative branch of topological graph theory. Enumeration formulas were developed for a large class of graph covering projections. The purpose of this paper is to count graph covering projections of graphs such that the corresponding covering space is a connected graph. The main tool of the enumeration is Pólya’s theorem.

It is well known that the chemical behavior of a compound is dependent upon the structure of itsmolecules. Quantitative structure – activity relationship (QSAR) studies and quantitative structure –property relationship (QSPR) studies are active areas of chemical research that focus on the nature ofthis dependency. Topological indices are the numerical value associated with chemical constitution...

: -We show how to construct a topological quantum field theory which corresponds to a given moduli space. We apply this method to the case of flat gauge connections defined over a Riemann surface and discuss its relations with the Chern-Simons theory and conformal field theory. The case of the SO(2,l) group is separately discussed. A topological field theory is linked to the moduli space of “se...

For any countable discrete group Γ (without further assumptions on it) we first construct an explicit morphism from the Left-Hand side of Baum-Connes assembly map, Ktop⁎(Γ), to periodic cyclic homology algebra, HP⁎(CΓ). This morphism, called Chern-Baum-Connes allows in particular give a proper and formulation for Chern-Connes pairingKtop⁎(Γ)×HP⁎(CΓ)⟶C. Several theorems are needed formulate map....

We present a topological Lagrangian field theory that is geometrically similar to Yang-Mills(-Higgs) theory, and study the Bogomol'nyi solitons contained within this theory. The topological field theory may provide an example of a dual field theory. The existence of a dual field theory to Yang-Mills(-Higgs) theory was conjectured by Montonen and Olive.

In [46], Witten related topological string theory on the cotangent bundle T M of a three manifold M to the Chern–Simons gauge theory on M . Gopakumar and Vafa [11] related the topological string theory on the deformed conifold (the cotangent bundle T S of the 3–sphere) to that on the resolved conifold (the total space of OP1. 1/ ̊OP1. 1/! P ). These works lead to a duality between the topologica...

For further studying the theory of multigranulation rough sets (MGRS), we attempt to investigate a new theory on multigranulation rough sets from the topological view in this paper. We firstly explore multigranulation topological rough space and its topological properties by giving some new definitions and theorems. Then, topological granularity and topological entropy are proposed to character...

I develop a formalism for solving topological field theories explicitly, in the case when the explicit expression of the instantons is known. I solve topological Yang-Mills theory with the k = 1 Belavin et al. instanton and topological gravity with the Eguchi-Hanson instanton. It turns out that naively empty theories are indeed nontrivial. Many unexpected interesting hidden quantities (puncture...