Related papers: Deformation of string topology into homotopy skein…

Chern-Simons theory in the 1/N expansion has been conjectured to be equivalent to a topological string theory. This conjecture predicts a remarkable relationship between knot invariants and Gromov-Witten theory. We review some basic aspects…

In the context of studying string backgrounds, much work has been devoted to the question of how similar a general quantum field theory (specifically, a two-dimensional superconformal theory) is to a sigma model. Put differently, one would…

Superconducting cosmic strings (SCSs) have received revived interests recently. In this paper we treat closed SCSs as oriented knotted line defects, and concentrate on their topology by studying the Hopf topological invariant. This…

We show that the space of chains of smooth maps from spheres into a fixed compact oriented manifold has a natural structure of a transversal $d$-algebra. We construct a structure of transversal 1-category on the space of chains of maps from…

In these lecture notes we discuss a body of work in which Morse theory is used to construct various homology and cohomology operations. In the classical setting of algebraic topology this is done by constructing a moduli space of graph…

In these lecture notes for the Les Houches School on Quantum Geometry I give an introductory overview of non-perturbative aspects of topological string theory. After a short summary of the perturbative aspects, I first consider the…

We give an introductory review of topological strings and their application to various aspects of superstrings and supersymmetric gauge theories. This review includes developing the necessary mathematical background for topological strings,…

We study string theory on orbifolds in the presence of an antisymmetric constant background field and discuss some of new aspects of the theory. It is shown that the term with the antisymmetric field has a topological nature like a…

In 1999 Chas and Sullivan discovered that the homology H_*(LX) of the space of free loops on a closed oriented smooth manifold X has a rich algebraic structure called string topology. They proved that H_*(LX) is naturally a…

The paper is concerned with cohomology of the small quantum group at a root of unity, and of its upper triangular subalgebra, with coefficients in a tilting module. We relate it to a certain t-structure on the derived category of…

Superstrings and topological strings with supermanifolds as target space play a central role in the recent developments in string theory. Nevertheless the rules for higher-genus computations are still unclear or guessed in analogy with…

We consider a string dual of a partially topological $U(N)$ Chern-Simons-matter (PTCSM) theory recently introduced by Aganagic, Costello, McNamara and Vafa. In this theory, fundamental matter fields are coupled to the Chern-Simons theory in…

We define string geometry: spaces of superstrings including the interactions, their topologies, charts, and metrics. Trajectories in asymptotic processes on a space of strings reproduce the right moduli space of the super Riemann surfaces…

We study a topological obstruction of a very stringy nature concerned with deforming the target space of an $N=2$ non-linear \sm. This target space has a singularity which may be smoothed away according to the conventional rules of geometry…

For M a closed, connected, oriented manifold, we obtain the Batalin-Vilkovisky (BV) algebra of its string topology through homotopy-theoretic constructions on its based loop space. In particular, we show that the Hochschild cohomology of…

We establish an equivalence between the stable category of coherent sheaves (satisfying a mild restriction) on a projective space and the homotopy category of a certain class of minimal complexes of free modules over the exterior algebra…

We argue that closed string tachyons drive two spacetime topology changing transitions -- loss of genus in a Riemann surface and separation of a Riemann surface into two components. The tachyons of interest are localized versions of…

This thesis presents several new insights on the interface between mathematics and theoretical physics, with a central role for fermions on Riemann surfaces. First of all, the duality between Vafa-Witten theory and WZW models is embedded…

We establish the general machinery of string topology for differentiable stacks. This machinery allows us to treat on an equal footing free loops in stacks and hidden loops. In particular, we give a good notion of a free loop stack, and of…

We survey several mathematical developments in the holonomy approach to gauge theory. A cornerstone of this approach is the introduction of group structures on spaces of based loops on a smooth manifold, relying on certain homotopy…