We discuss unifying features of topological field theories in 2, 3 and 4 dimensions. This includes relations among enumerative geometry (2d topological field theory) link invariants (3d Chern-Simons theory) and Donaldson invariants (4d topological theory). (Talk presented in conference on Geometry and Topology in honor of M. Atiyah, R. Bott, F. Hirzebruch and I. Singer, Harvard University, May ...

Stony Brook IMS Preprint #2008/4 September 2008 Abstract. Regluing is a topological operation that helps to construct topological models for rational functions on the boundaries of certain hyperbolic components. It also has a holomorphic interpretation, with the flavor of infinite dimensional Thurston–Teichmüller theory. We will discuss a topological theory of regluing, and trace a direction in...

We describe a topological string theory which reproduces many aspects of the 1/N expansion of SU(N) Yang-Mills theory in two spacetime dimensions in the zero coupling (A = 0) limit. The string theory is a modified version of topological gravity coupled to a topological sigma model with spacetime as target. The derivation of the string theory relies on a new interpretation of Gross and Taylor’s ...

We analyze the topological nature of c = 1 string theory at the self–dual radius. We find that it admits two distinct topological field theory structures characterized by two different puncture operators. We show it first in the unperturbed theory in which the only parameter is the cosmological constant, then in the presence of any infinitesimal tachyonic perturbation. We also discuss in detail...

It is argued that gravitational descendants in the theory of topological gravity coupled to topological Landau-Ginzburg theory can be constructed from matter fields alone (without metric fields and ghosts).In this sense topological gravity is ”induced”. We discuss the mechanism of this effect(that turns out to be connected with K.Saito’s higher residue pairing: K(σi(Φ1),Φ2) = K(Φ1,Φ2) , and dem...

These are expository lectures reviewing (1) recent developments in two-dimensional YangMills theory and (2) the construction of topological field theory Lagrangians. Topological field theory is discussed from the point of view of infinite-dimensional differential geometry. We emphasize the unifying role of equivariant cohomology both as the underlying principle in the formulation of BRST transf...

Two-dimensional fermionic string theory is shown to have a structure of topological model, which is isomorphic to a tensor product of two topological ghost systems independent of each other. One of them is identified with c = 1 bosonic string theory while the other has trivial physical contents. This fact enables us to regard two-dimensional fermionic string theory as an embedding of c = 1 boso...

In this paper we develop the theory of topological categories over a base category, that is, a theory of topological functors. Our notion of topo-logical functor is similar to (but not the same) the existing notions in the literature (see [2] 7.3), and it aims at the same examples. In our sense, a (pre) topological functor is a functor that creates cartesian families. A topological functor is, ...