相关论文: A hitchhiker's guide to Khovanov homology

These lecture notes, which were designed for the Summer School "Heegaard-Floer Homology and Khovanov Homology" in Marseilles, 29th May - 2nd June, 2006, provide an elementary introduction to Khovanov homology. The intended audience is…

This is an expository paper discussing various versions of Khovanov homology theories, interrelations between them, their properties, and their applications to other areas of knot theory and low-dimensional topology.

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…

These lecture notes (from the Second Autumn School in High Energy Physics and Quantum Field Theory, Yerevan 2014) cover a number of topics related to geometric quantization. Most of the material is presented from a physicist's point of…

By adding or removing appropriate structures to Gauss diagram, one can create useful objects related to virtual links. In this paper few objects of this kind are studied: twisted virtual links generalizing virtual links; signed chord…

These notes cover the lectures of the first named author at 2021 IHES Summer School on "Enumerative Geometry, Physics and Representation Theory" with additional details and references. They cover the definition of Khovanov-Rozansky triply…

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…

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…

We introduce Khovanov homology for ribbon graphs and show that the Khovanov homology of a certain ribbon graph embedded on the Turaev surface of a link is isomorphic to the Khovanov homology of the link (after a grading shift). We also…

These are lecture notes from a series of lectures at the SMF summer school on "Geometric and Quantum Topology in Dimension 3", June 2014. The focus is on Heegaard Floer homology from the perspective of sutured Floer homology.

These are lecture notes on Floer and Rabinowitz-Floer homology written for a graduate course at UNICAMP August-December 2016 and a mini-course held at IMPA in August 2017.

We modify the definition of the Khovanov complex for oriented links in a thickening of an oriented surface to obtain a triply graded homological link invariant with a new homotopical grading.

In these notes, I will sketch a new approach to Khovanov homology of knots and links based on counting the solutions of certain elliptic partial differential equations in four and five dimensions. The equations are formulated on four and…

In the first of these two lectures, I use a comparison to symplectic Khovanov homology to motivate the idea that the Jones polynomial and Khovanov homology of knots can be defined by counting the solutions of certain elliptic partial…

We show that the unnormalised Khovanov homology of an oriented link can be identified with the derived functors of the inverse limit. This leads to a homotopy theoretic interpretation of Khovanov homology.

We refine Khovanov homology in the presence of an involution on the link. This refinement takes the form of a triply-graded theory, arising from a pair of filtrations. We focus primarily on strongly invertible knots and show, for instance,…

The papers math.QA/0403527 and math.QA/0409414 v.1 are now merged together. The final version is available at math.QA/0409414 v.2. To avoid duplication of papers, math.QA/0403527 is now removed.

In the present paper, we construct the Khovanov homology theory for virtual links. Besides the direct approach with Z_{2} coefficients we also describe the Khovanov homology for framed links and the Khovanov homology using ``double cover''.…

This article is an elaboration of a talk given at an international conference on Operator Theory, Quantum Probability, and Noncommutative Geometry held during December~20--23, 2004, at the Indian Statistical Institute, Kolkata. The lecture…

In this short note we provide a review of some developments in the area of homotopy quantum field theories, loosely based on a talk given by the second author at the Xth Oporto Meeting on Geometry, Topology and Physics.