Related papers: Geometric proof of Thom conjecture
We present a geometric approach to the Baum-Connes conjecture with coefficients for Gromov monster groups via a theorem of Khoskham and Skandalis. Secondly, we use recent results concerning the a-T-menability at infinity of large girth…
From Khovanov homology, we extract a new lower bound for the Gordian distance of knots, which combines and strengthens the previously existing bounds coming from Rasmussen invariants and from torsion invariants. We also improve the bounds…
We investigate the famous conjecture by Erd\H os-Simonovits and Sidorenko using information theory. Our method gives a unified treatment for all known cases of the conjecture and it implies various new results as well. Our topological type…
We use plumbing calculus to prove the homotopy commutativity assertion of the Geometric P=W conjecture in all Painlev\'e cases. We discuss the resulting Mixed Hodge structures on Dolbeault and Betti moduli spaces.
We introduce an analogue of the Novikov Conjecture on higher signatures in the context of the algebraic geometry of (nonsingular) complex projective varieties. This conjecture asserts that certain "higher Todd genera" are birational…
Given a link or a tangle diagram, we define algorithmic Morse theoretic simplifications on their Khovanov homology. In contrast to Bar-Natan's scanning algorithm, the cancellations are postponed until the end and performed in one go.…
In 1992, Wilf and Zeilberger conjectured that a hypergeometric term in several discrete and continuous variables is holonomic if and only if it is proper. Strictly speaking the conjecture does not hold, but it is true when reformulated…
In this paper we complete the proof began by A. Polishchuk and E. Zaslow (math.AG/9801119) of a weak version of Kontsevich's homological mirror symmetry conjecture for elliptic curves. The main difference to the work of Polishchuk and…
We show a new, elementary and geometric proof of the classical Alexandrov theorem about the second order differentiability of convex functions. We also show new proofs of recent results about Lusin approximation of convex functions and…
We present a direct proof of the second conjecture made by M. Atiyah and P. Sutcliffe for the case of convex quadrilaterals. Unlike previous work on this conjecture, our proof does not require any computer aided computations. The new proof…
This paper has been withdrawn by the author, due to a crucial error in page 5.
We adapt Bar-Natan's scanning algorithm for fast computations in (even) Khovanov homology to odd Khovanov homology. We use a mapping cone construction instead of a tensor product, which allows us to deal efficiently with the more…
In the paper, we give a Schur-Toponogov theorem in Riemannian geometry, which not only generalizes Schur's and Toponogov's theorem but also indicates their relation. Inspired by its proof, we also supply a new proof of Toponogov's theorem…
This paper has been withdrawn by the author due to a serious gap in the proof of the main theorem.
We give an alternative proof of Madsen-Weiss' generalized Mumford conjecture. Our proof is based on ideas similar to Madsen-Weiss' original proof, but it is more geometrical and less homotopy theoretical in nature. At the heart of the…
The Manin-Mumford conjecture in characteristic zero was first proved by Raynaud. Later, Hrushovski gave a different proof using model theory. His main result from model theory, when applied to abelian varieties, can be rephrased in terms of…
We prove a conjecture of Migdail and Wehrli regarding the odd Khovanov cobordism maps associated to knotted spheres. Our key tool is Daemi's plane Floer homology, which we use in place of a Lee deformation. Continuing the analogy with Lee…
We present a new solution to the formality problem for the framed Goldman--Turaev Lie bialgebra, constructing Goldman-Turaev homomorphic expansions (formality isomorphisms) from the Kontsevich integral. Our proof uses a three dimensional…
Given a group, we construct a fundamental additive functor on its orbit category. We prove that any isomorphism conjecture valid for this fundamental isomorphism functor holds for all additive functors, like K-theory, cyclic homology,…
We correct a mistake regarding almost complex structures on Hilbert schemes of points in surfaces in arXiv:1510.02449. The error does not affect the main results of the paper, and only affects the proofs of invariance of equivariant…