In cohomological field theory we can obtain topological invariants as correlation functions of BRS cohomology classes. A proper understanding of BRS cohomology which gives non-trivial results requires the equivariant cohomology theory. Both topological Yang-Mills theory and topological string theory are typical examples of this fact. After reviewing the role of the equivariant cohomology in top...

This thesis presents Topological Domain Theory as a powerful and flexible framework for denotational semantics. Topological Domain Theory models a wide range of type constructions and can interpret many computational features. Furthermore, it has close connections to established frameworks for denotational semantics, as well as to well-studied mathematical theories, such as topology and computa...

qspr study on benzene derivatives have been made using recently introduced topological methodology. in this study the relationship between the randic' (x'), balaban (j), szeged (sz),harary (h), wiener (w), hyperwiener and wiener polarity (wp) to the thermal energy (eth), heat capacity (cv) and entropy (s) of benzene derivatives is represented.physicochemical properties are taken from the quantu...

‎In the present paper‎, ‎we are going to use geometric and topological concepts‎, ‎entities and properties of the‎ ‎integral curves of linear vector fields‎, ‎and the theory of differential equations‎, ‎to establish a representation for some groups on $R^{n} (ngeq 1)$‎. ‎Among other things‎, ‎we investigate the surjectivity and faithfulness of the representation‎. At the end‎, ‎we give some app...

In this paper, we describe a technique, with roots in topological graph theory, that we call rind modeling. It provides for the easy creation of surfaces resembling peeled and punctured rinds. We show how the method’s two main steps of 1) creation of a shell or crust like the rind of an orange, and 2) opening holes in the crust by punching or peeling can be encapsulated into a real time semi-au...

Finite simple graphs are a playground for classical areas of mathematics. We illustrate this by looking at some results.

A Heffter array is an m× n matrix with nonzero entries from Z2mn+1 such that i) every row and column sum to 0, and ii) exactly one of each pair {x,−x} of nonzero elements appears in the array. We construct some Heffter arrays. These arrays are used to build current graphs used in topological graph theory. In turn, the current graphs are used to embed the complete graph K2mn+1 so that the faces ...

We identify and examine a generalization of topological sigma models suitable for coupling to topological open strings. The targets are Kähler manifolds with a real structure, i.e. with an involution acting as a complex conjugation, compatible with the Kähler metric. These models satisfy axioms of what might be called “equivariant topological quantum field theory,” generalizing the axioms of to...