Related papers: Notes on topological strings and knot contact homo…
These notes on string theory are based on a series of talks I gave during my graduate studies. As the talks, this introductory essay is intended for young students and non-string theory physicists.
A string-theoretic structure of the standard model is defined having a 4-D quantum gravity metric consistent with topological and algebraic first principles. Unique topological diagrams of string states, strong and weak interactions and…
Knot contact homology is an ambient isotopy invariant of knots and links in $\mathbb R^3$. The purpose of this paper is to extend this definition to an ambient isotopy invariant of tangles and prove that gluing of tangles gives a gluing…
We summarize recent work on a combinatorial knot invariant called knot contact homology. We also discuss the origins of this invariant in symplectic topology, via holomorphic curves and a conormal bundle naturally associated to the knot.
I present arguments to the affect that the topological phase of string theory must be event-symmetric. This motivates a search for a universal string group for discrete strings in event-symmetric space-time which unifies space-time symmetry…
We extend knot contact homology to a theory over the ring $\mathbb{Z}[\lambda^{\pm 1},\mu^{\pm 1}]$, with the invariant given topologically and combinatorially. The improved invariant, which is defined for framed knots in $S^3$ and can be…
These notes are an expanded version of an introductory lecture on contact geometry given at the 2001 Georgia Topology Conference. They are intended to present some of the "topological" aspects of three dimensional contact geometry.
We study the relation between topological string theory and singularity theory using the partition function of $A_{N-1}$ topological string defined by matrix integral of Kontsevich type. Genus expansion of the free energy is considered, and…
We describe two major string topology operations, the Chas-Sullivan product and the Goresky-Hingston coproduct, from geometric and algebraic perspectives. The geometric construction uses Thom-Pontrjagin intersection theory while the…
In this note we present a brief overview of connections between Chern-Simons theory and topological strings. A prominent role in this link has been played by large N dualities and holography. We demystify this by explaining why the Kahler…
A formal relationship between scattering amplitudes in critical bosonic string theory and correlation functions of operators in topological string theory is found.
These notes follow a lecture series at the "Singularities and low dimensional topology" winter school at the R\'enyi Institute in January 2023, with a target audience of graduate students in singularity theory and low-dimensional topology.…
Knot, link, and tangle theory is crucial in both mathematical theory and practical application, including quantum physics, molecular biology, and structural chemistry. Unlike knots and links, tangles impose more relaxed constraints,…
These lecture notes are meant to serve as an introduction to some geometric constructions and techniques (in particular the ones of toric geometry) often employed by the physicist working on string theory compactifications. The emphasis is…
I present a new class of topological string theories, and discuss them in two dimensions as candidates for the string description of large-$N$ QCD. The starting point is a new class of topological sigma models, whose path integral is…
In this expository paper we discuss a project regarding the string topology of a manifold, that was inspired by recent work of Moore-Segal, Costello, and Hopkins and Lurie, on "open-closed topological conformal field theories". Given a…
A homology and cohomology theory for topological quandles are introduced. The relation between these (co)homology groups and quandle (co)homology groups are studied. The 1 - topological quandle cocycles are used to compute state sum…
We review recent developments in the theory of Thompson group representations related to knot theory.
Recent progress in string theory has led to a reformulation of quantum-group polynomial invariants for knots and links into new polynomial invariants whose coefficients can be understood in topological terms. We describe in detail how to…
This thesis is concerned with a realisation of topological theories in terms of statistical models known as Calabi-Yau crystals. The thesis starts with an introduction and review of topological field and string theories. Subsequently…