Related papers: Geometric proof of Thom conjecture
Using geometric homology and cohomology we give a simple and conceptual proof of the Thom isomorphism theorem.
This paper has been withdrawn by the author due to an error in the proof of Theorem 1.
We disprove the conjecture of M. Khovanov (math.QA/9908171) on the functoriality of his link homology with polynomial coefficients. This is in contrast to the case of integer coefficients, where functoriality was proved in math.GT/0206303 .
We show that Khovanov homology and Hochschild homology theories share common structure. In fact they overlap: Khovanov homology of a $(2,n)$-torus link can be interpreted as a Hochschild homology of the algebra underlining the Khovanov…
This note is an exposition of the proof of Thom's conjecture by Kronheimer and Mrowka, using the new Seiberg-Witten invariants.
We study Thom Transversality Theorem using a point of view, suggested by Gromov, which allows to avoid the use of Sard Theorem and gives finer informations on the structure of the set of non-transverse maps.
The goal of this paper is to prove the full geometric Bogomolov conjecture. We first reduce it to the case that the extension of the base fields has transcendence degree 1, and then we prove the later case by intersection theory in…
This paper has been withdrawn by the author due to a crucial sign error in Theorem 3.4.
We give a simple proof of the smooth Thom isomorphism for complex bundles for the bivariant K-theories on locally convex algebras considered by Cuntz. We also prove the Thom isomorphism in Kasparov's KK-theory in a form stated without proof…
This is a survey paper of the developments on the geometric Bogomolov conjecture. We explain the recent results by the author as well as previous works concerning the conjecture. This paper also includes an introduction to the height theory…
This paper has been withdrawn by the authors due to crucial error in the main proof (located in Section 2.4). The authors apologize for any inconveniences.
Khovanov homology is functorial up to sign with respect to link cobordisms. The sign indeterminacy has been fixed by several authors, by extending the original theory both conceptually and algebraically. In this paper we propose an…
This paper has been withdrawn by the author due to a critical error in the proof of Theorem A pointed out by Burkhard Wilking.
We show that reduced Khovanov homology over any field is invariant under component-preserving Conway mutation. Our proof relies on strong geography restrictions for a certain Khovanov multicurve invariant associated with Conway tangles that…
We prove the Strengthened Hanna Neumann Conjecture, in its common graph theoretic formulation. Our original approach to this conjecture used cohomology of sheaves on graphs, although here we give a short combinatorial proof that we found in…
In 1989 H. Tverberg proposed a quite general conjecture in Discrete geometry, which could be considered as the common basis for many results in Combinatorial geometry and at the same time as a discrete analogue of the common transversal…
We prove a new inequality relating volume to length of closed geodesics on area minimizers for generic metrics on the complex projective plane. We exploit recent regularity results for area minimizers by Moore and White, and the…
This paper has been withdrawn by the author, due to a crucial error in the proof of Thm.1
This article contains a complete proof of Gabrielov's rank Theorem, a fundamental result in the study of analytic map germs. Inspired by the works of Gabrielov and Tougeron, we develop formal-geometric techniques which clarify the difficult…
This paper has been withdrawn by the author due to the version of [A complete proof of Hamilton's conjecture] at arXiv:1008.1576