Related papers: Notes on topological strings and knot contact homo…

This is a survey article on the recent development of "stringy geometry and topology of orbifolds", a new subject of mathematics motivated by orbifold string theory.

In these lecture notes for the Les Houches School on Applications of Random Matrices in Physics we give an introduction to the connections between matrix models and topological strings. We first review some basic results of matrix model…

We give a fresh introduction to the Khovanov Homology theory for knots and links, with special emphasis on its extension to tangles, cobordisms and 2-knots. By staying within a world of topological pictures a little longer than in other…

Cosmic strings in the early universe have received revived interest in recent years. In this paper we derive these structures as topological defects from singular distributions of the quintessence field of dark energy. Our emphasis is…

I review recent progress on the connection between string theory and quantum chromodynamics in the context of the gauge/gravity duality. Emphasis is placed on conciseness and conceptual aspects rather than on technical details. Topics…

These are notes of a series of lectures on mirror symmetry and topological string theory given at the Mathematical Sciences Center at Tsinghua University. The N=2 superconformal algebra, its deformations and its chiral ring are reviewed. A…

It is sometimes said that there may be a unique algebraic theory independent of space-time topologies which underlies superstring and p-brane theories. In this paper, I construct some algebras using knot relations within the framework of…

A review on topological strings and the geometry of the space of two dimensional theories. (Lectures given by C. Gomez at the Enrico Fermi Summer School, Varenna, July 1994)

We consider a string theory with two types of strings with geometric interaction. We show that the theory contains strings with constant Dirichlet boundary condition and those strings are glued together by 2-d topological gravity with…

Besides offering a friendly introduction to knot homologies and quantum curves, the goal of these lectures is to review some of the concrete predictions that follow from the physical interpretation of knot homologies. In particular, this…

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…

In this thesis we probe various interactions between toric geometry and string theory. First, the notion of a top was introduced by Candelas and Font as a useful tool to investigate string dualities. These objects torically encode the local…

Relations between the string topology of Chas and Sullivan and the homotopy skein modules of Hoste and Przytycki are studied. This provides new insight into the structure of homotopy skein modules and their meaning in the framework of…

The purpose of this paper is to discuss how topology and geometry provide, in many instances, the connective tissue that enables logical comprehension. We illustrate this theme with many examples including Venn diagrams, knot diagrams,…

String theory provides the only consistent framework so far that unifies all interactions including gravity. We discuss gravity and cosmology in string theory. Conventional notions from general relativity like geometry, topology etc. are…

Link homology theories (such as knot Floer homology and Khovanov homology) have become indispensable tools for studying knots and links, including powerful 4-dimensional obstructions. These notes, based on lectures given at the 2024 Georgia…

Recently there had been a great deal of activity associated with various schemes of designing both analytical and experimental methods describing knotted structures in electrodynamics and in hydrodynamics.The majority of works in…

In these lectures, we review the main properties of the topological theory obtained by twisting the N=2 two-dimensional superconformal algebra, associated to supersymmetric string compactifications. In particular, we describe a set of…

The homology of a 2-colored dioperad of decorated Riemann surfaces, relevant to open-closed string field theory, is computed. The structure it describes is realized in an open-closed setting of string topology via an action at the level of…

In this paper we study the string topology (\'a la Chas-Sullivan) of an orbifold. We define the string homology ring product at the level of the free loop space of the classifying space of an orbifold. We study its properties (introducing…