Related papers: Multidimensional $C^0$ transversality and the shad…

A very short proof of the following smooth homogeneity theorem of D. Repovs, E. V. Scepin and the author is presented. Let N be a locally compact subset of a smooth manifold M. Assume that for each two points x,y in N there exist their…

We prove the Demailly--Peternell--Schneider conjecture in positive characteristic: if $X$ is a smooth projective variety over an algebraically closed field of characteristic $p>0$ with $-K_X$ is nef, then the Albanese morphism $a: X \to A$…

We consider the dependence on parameters of the solutions of cohomology equations over Anosov diffeomorphisms. We show that the solutions depend on parameters as smoothly as the data. As a consequence we prove optimal regularity results for…

We show generic $C^\infty$ hyperbolic flows (Axiom A and no cycles, but not transitive Anosov) commute with no $C^\infty$-diffeomorphism other than a time-t map of the flow itself. Kinematic expansivity, a substantial weakening of…

The main purpose of this paper is to carry out some of the foundational study of $C^0$-Hamiltonian geometry and $C^0$-symplectic topology. We introduce the notions of the strong and the weak {\it Hamiltonian topology} on the space of…

We prove that the group of contact diffeomorphisms is closed in the group of all diffeomorphisms in the C^0-topology. By Gromov's alternative, it suffices to exhibit a diffeomorphism that can not be approximated uniformly by contact…

Given a connected and locally compact Hausdorff space X with a good base K we assign, in a functorial way, a C(X)-algebra to any precosheaf of C*-algebras A defined over K. Afterwards we consider the representation theory and the Kasparov…

Given a stratified variety X with strata satisfying a cohomological parity-vanishing condition, we define and show the uniqueness of "parity sheaves", which are objects in the constructible derived category of sheaves with coefficients in…

In terms of Turaev's shadows, we provide a sufficient condition for a compact, smooth, acyclic 4-manifold with boundary the 3-sphere to be diffeomorphic to the standard 4-ball. As a consequence, we prove that if a compact, smooth, acyclic…

Supersymmetric states in M-theory are mapped after compactification to perturbatively non-supersymmetric states in type IIA string theory, with the supersymmetric parts being encoded in the non-perturbative section of the string theory. An…

Voevodsky outlined a conjectural programme that his slice filtration in motivic homotopy theory should give rise to a good theory of $\mathbb{A}^1$-invariant motivic cohomology. This paper achieves his vision in the generality of arbitrary…

It is an elementary fact that the action by holomorphic automorphisms on C^n is infinitely transitive, i.e., m-transitive for any m in N. The same holds on any Stein manifold with the holomorphic density property X. We study a parametrized…

Let X be a space, intended as a possibly curved spacetime, and A a precosheaf of C*-algebras on X. Motivated by algebraic quantum field theory, we study the Kasparov and Theta-summable K-homology of A interpreting them in terms of the…

We discuss the concept of the shadow boundary of a centrally symmetric convex ball $K$ (actually being the unit ball of a Minkowski normed space) with respect to a direction ${\bf x}$ of the Euclidean n-space $R^n$. We introduce the concept…

We study a number of questions related to the $C^0$-topology of contactomorphisms and contact homeomorphisms. In particular, we show a connection between Rokhlin property of contact homeomorphisms and contact non-squeezing, we define a new…

We explicitly describe cohomology of the sheaf of differential forms with poles along a semiample divisor on a complete simplicial toric variety. As an application, we obtain a new vanishing theorem which is an analogue of the…

Dynamical quantum field theories (QFTs), such as those in which spacetimes are equipped with a metric and/or a field in the form of a smooth map to a target manifold, can be formulated axiomatically using the language of…

We show that for any Riemannian foliation with a simply connected and negatively curved leaf space the normal exponential map of a leaf is a diffeomorphism. As an application, if the leaves are furthermore minimal submanifolds, we give a…

We study the relation between the shadowing property and the limit shadowing property. We prove that if a continuous self-map $f$ of a compact metric space has the limit shadowing property, then the restriction of $f$ to the non-wandering…

We prove that in closed almost complex manifolds of any dimension, generic perturbations of the almost complex structure suffice to achieve transversality for all unbranched multiple covers of simple pseudoholomorphic curves with…