Related papers: Univalent completion
By careful analysis of the comparison map from a simplicial set to its image under Kan's ex-infinity functor we obtain a new and combinatorial proof that it is a weak homotopy equivalence. Moreover, we obtain a presentation of it as a…
Let X be a compact K\"ahler manifold such that the universal cover admits a compactification. We conjecture that the fundamental group is almost abelian and reduce it to a classical conjecture of Iitaka.
Theorem (uniformization). Let X be a compact Kahler manifold of dimension n with large, residually finite and nonamenable fundamental group. Then its universal covering is a bounded domain in the n-dimensional affine space.
We introduce the notion of algebraic fibrant objects in a general model category and establish a (combinatorial) model category structure on algebraic fibrant objects. Based on this construction we propose algebraic Kan complexes as an…
We classify singular fibres of a projective Lagrangian fibration over codimension one points. As an application, we obtain a canonical bundle formula for a projective Lagrangian fibration over a smooth manifold.
We present a slight generalization of the notion of completely integrable systems to get them being integrable by quadratures. We use this generalization to integrate dynamical systems on double Lie groups.
We consider embeddings of a finite complex in a sphere. We give a homotopy theoretic classification of such embeddings in a wide range.
We present a comprehensive classification theory for saturated Fell bundles over locally compact groups, utilizing data associated with their base group and unit fiber. This framework offers a unified approach to understanding the structure…
This article generalises to K\"ahler orbifolds general results on uniformisation of compact K\"ahler manifolds such as the Shafarevich conjecture for linear fundamental groups.
We give an elementary construction of the dual fibration of a fibration. It does not use the non-elementary notion of (pseudo-) functor into the category of categories.
We prove a general statement about the integrality of the sequences generated by a recursion of the following form: $nu_n$ equals a linear combination of $u_{n-1},u_{n-2},\dots,u_0$ with polynomial coefficients in $n$ of special form. This…
In this paper, we show that any compact manifold that carries a SL(n;R)-foliation is fibered on the circle S^1.
In the paper we introduce the notions of a singular fibration and a singular Seifert fibration. These notions are natural generalizations of the notion of a locally trivial fibration to the category of stratified pseudomanifolds. For…
Let $S$ be a semigroup, let $n\in\mathbb{N}$ be a positive natural number, let $A,B\subseteq S$, let $\mathcal{U},\mathcal{V}\in\beta S$ and let let $\mathcal{F}\subseteq\{f:S^{n}\rightarrow S\}$. We say that $A$ is $\mathcal{F}$-finitely…
We investigate the existence, and lack of unicity, of a holomorphic fibration by discs transversal to a rational curve in a complex surface.
In this note we introduce a notion of free cofibrations of permutative categories. We show that each cofibration of permutative categories is a retract of a free cofibration.
We characterize unitary representations of braid groups $B_n$ of degree linear in $n$ and finite images of such representations of degree exponential in $n$.
We introduce the abstract notion of a closed necklical set in order to describe a functorial combinatorial model of the free loop fibration $\Omega Y\rightarrow \Lambda Y\rightarrow Y$ over the geometric realization $Y=|X|$ of a path…
We present a substantial generalisation of a classical result by Lie on integrability by quadratures. Namely, we prove that all vector fields in a finite-dimensional transitive and solvable Lie algebra of vector fields on a manifold can be…
We investigate birational boundedness of Fano varieties and Fano fibrations. We establish an inductive step towards birational boundedness of Fano fibrations via conjectures related to boundedness of Fano varieties and Fano fibrations. As…