Related papers: A homotopy theorem for Oka theory

We present a short proof of Szemer\'edi's Theorem using a dynamical system enriched by ideas from model theory. The resulting proof contains features reminiscent of proofs based on both ergodic theory and on hypergraph regularity.

The Hopf theorem states that homotopy classes of continuous maps from a closed connected oriented smooth $n$-manifold $M$ to the $n$-sphere are classified by their degree. Such a map is equivalent to a section of the trivial $n$-sphere…

We prove a gap rigidity theorem for diagonal curves in irreducible compact Hermitian symmetric spaces of tube type, which is a dual analogy to a theorem obtained by Mok in noncompact case. Motivated by the proof we give a theorem on weaker…

We construct a model category (in the sense of Quillen) for set theory, starting from two arbitrary, but natural, conventions. It is the simplest category satisfying our conventions and modelling the notions of finiteness, countability and…

We investigate the behaviour of the Oka property with respect to deformations of compact complex manifolds. We show that in a family of compact complex manifolds, the set of Oka fibres corresponds to a G-delta subset of the base. We give a…

In this book we prove unified classification results for equivariant principal bundles when the topological structure group is truncated. The conceptually transparent proof invokes a smooth Oka principle, which becomes available after…

We give geometric proofs for Grobman-Hartman theorem for diffeomorphisms and ODEs. Proofs use covering relations and cone conditions for maps and isolating segments and cone condition for ODEs. We prove also the H\"older condition for the…

Like categories, small 2-categories have well-understood classifying spaces. In this paper, we deal with homotopy types represented by 2-diagrams of 2-categories. Our results extend to homotopy colimits of 2-functors lower categorical…

We give a concise proof of the fundamental theorem of smoothing theory in the special case when a smoothing exists.

Our main theorem states that the complement of a compact holomorphically convex set in a Stein manifold with the density property is an Oka manifold. This gives a positive answer to the well-known long-standing problem in Oka theory whether…

We prove a version of Gromov's compactness theorem for pseudo-holomorphic curves which holds locally in the target symplectic manifold. This result applies to sequences of curves with an unbounded number of free boundary components, and in…

We present a proof of the Chevalley-Weil Theorem that is somewhat different from the proofs appearing in the literature and with somewhat weaker hypotheses, of purely topological type. We also provide a discussion of the assumptions, and an…

Finite \'etale covers of a connected scheme $X$ are parametrised by the \'etale fundamental group via the monodromy correspondence. This was generalised to an exodromy correspondence for constructible sheaves, first in the topological…

In this paper, we introduce geometric technique of working with skew-framed manifolds. It allows us to study stable homotopy groups of some Thom spaces by geometric means. We schematically describe how our results (which are also of…

We prove the parametric homotopy principle for holomorphic immersions of Stein manifolds into Euclidian space and the homotopy principle with approximation on holomorphically convex sets. We write an integration by parts like formula for…

We first exhibit counterexamples to some open questions related to a theorem of Sakai. Then we establish an extension theorem of Sakai type for separately holomorphic/meromorphic functions.

Homotopy connectedness theorems for complex submanifolds of homogeneous spaces (sometimes referred to as theorems of Barth-Lefshetz type) have been established by a number of authors. Morse Theory on the space of paths lead to an elegant…

Homotopical localizations with respect to (possibly proper) classes of maps are known to exist assuming the validity of a large-cardinal axiom from set theory called Vop\v{e}nka's principle. In this article, we prove that each of the…

We generalize several comparison results between algebraic, semi-topological and topological K-theories to the equivariant case with respect to a finite group.

We initiate the study of sheaves on Cech closure spaces, providing a new, unified approach to sheaf theory on many of the major classes of spaces of interest to applications: topological spaces, finite simplicial complexes (seen as $T_0$…