Related papers: Turaev Surfaces
Draft version of an article prepared for the Encyclopedia of Mathematical Physics, Elsevier, to appear in 2006.
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…
Due to the recent renewal in the interest for embedded surfaces we provide a list of commented references of interest.
This is a survey paper on Legendrian and transversal knots for Handbook of Knot Theory.
This is a survey article to be part of the Encyclopedia of Mathematical Physics, to be published by Elsevier in the beginning of 2006.
The surface science of iron oxides is comprehensively reviewed. For the full abstract please see pdf.
This note points out a gap in the proof of the main theorem of the article "Birationally rigid hypersurfaces" published in Invent. Math. 192 (2013), 533-566, and provides a new proof of the theorem.
This article was originally published in Topology 31 (1992). The present hyperTeXed redaction corrects a few typographical errors and updates the references.
This is a brief introduction to the theory of Enriques surfaces over arbitrary algebraically closed fields. Some new results about automorphism groups of Enriques surfaces are also included.
This book is a detailed introduction to the theory of finite type (Vassiliev) knot invariants, with a stress on its combinatorial aspects. It is intended to serve both as a textbook for readers with no or little background in this area, and…
Short survey to be published at the Encyclopedia of Mathematical Physics.
This paper (written in Russian) presents a survey of new and earlier results on fine zonotopal tilings (briefly, cubillages) of cyclic zonotopes. The combinatorial theory of these objects is of interest in its own right and also has a…
This survey of some of the more topological aspects of the placement problem for complex curves in complex surfaces was originally published in L'Enseignement Mathematique 29 (1983). The present LaTeXed redaction corrects several…
The present paper is an addendum to "Spherical structures on torus knots and links", arXiv:1008.0312, and concerns more general case of torus knot and link cone-manifolds.
The toric surfaces for octonions and related objects are discussed.
This is an expository paper about the topics listed in the title.
This is an expository paper which presents the holomorphic classification of rational complex surfaces from a simple and intuitive point of view, which is not found in the literature. Our approach is to compare this classification with the…
In these expository notes, we give a proof of regularity of Anosov splitting for Anosov diffeomorphisms in a torus. We also generalize the idea to higher dimensions and to Anosov flows.
We introduce a relation of cobordism for knots in thickened surfaces and study cobordism invariants of such knots.
In this revised version, we add some expository material and references and make some minor corrections.