Related papers: Skeletal maps and I-favorable spaces

In this note we provide a direct proof of the complete classification of conformally flat isoparametric submanifolds of Euclidean space.

We prove that every continuous map from a Stein manifold X to a complex manifold Y can be made holomorphic by a homotopic deformation of both the map and the Stein structure on X. In the absence of topological obstructions the holomorphic…

The class of Hausdorff spaces that are continuous images of compact orderable spaces is studied by analyzing the relationship between the elements of this class and compact orderable spaces in a back-and-forth fashion. Structure results for…

Spaces with positive weights are those whose rational homotopy type admits a large family of "rescaling" automorphisms. We show that finite complexes with positive weights have many genuine self-maps. We also fix the proofs of some previous…

This note contains a Stone-style representation theorem for compact Hausdorff spaces.

We introduce the notion of compactifiable classes -- these are classes of metrizable compact spaces that can be up to homeomorphic copies ``disjointly combined'' into one metrizable compact space. This is witnessed by so-called compact…

For any infinite-type surface $S$, a natural question is whether the homology of its mapping class group contains any non-trivial classes that are supported on (i) a compact subsurface or (ii) a finite-type subsurface. Our purpose here is…

We define the notion of a hierarchically cocompact classifying space for a family of subgroups of a group. Our main application is to show that the mapping class group $\mbox{Mod}(S)$ of any connected oriented compact surface $S$, possibly…

We prove that the space of surjective holomorphic maps from a compact complex manifold to a compact K\"ahler manifold with trivial canonical class and finite fundamental group is discrete.

Assume hat a functionally Hausdorff space $X$ is a continuous image of a \v{C}ech complete space $P$ with Lindel\"of number $l(P)<\mathfrak c$. Then the following conditions are equivalent: (i) every compact subset of $X$ is scattered, (ii)…

A relatively simple algebraic framework is given, in which all the compact symmetric spaces can be described and handled without distinguishing cases. We also give some applications and further results.

We give algebraic characterizations of the type I and CCR properties for locally compact second countable, ample Hausdorff groupoids in terms of subquotients of their Boolean inverse semigroups of compact open bisections. It yields in turn…

We construct a category that classifies compact Hausdorff spaces by their shape and finite topological spaces by their weak homotopy type.

We prove that Banach spaces with a $1$-projectional skeleton form a $\mathcal{P}$-class and deduce that any such space admits a strong Markushevich basis. We provide several equivalent characterizations of spaces with a projectional…

We construct proper good moduli spaces for moduli stacks of Bridgeland semistable orthosymplectic complexes on a complex smooth projective variety, which we propose as a candidate for compactifying moduli spaces of principal bundles for the…

We give a necessary and sufficient condition for a set of left invariant metrics on a compact Heisenberg manifold to be relatively compact in the corresponding moduli space.

Given a hypersurface in a complex projective space, we prove that the multidegrees of its toric polar map agree, up to sign, with the coefficients of the Chern-Schwartz-MacPherson class of a distinguished open set, namely the complement of…

We show that the inverse limit and the orbit map commute for actions of compact groups on compact Hausdorff spaces.

We show that one can characterize the Besov spaces on a smooth compact oriented Riemannian manifold, for the full range of indices, through a knowledge of the size of frame coefficients, using the frames we have constructed in [8].

Explicit bases for the spaces of holomorphic cusp forms of all even positive weights and all orders are constructed. The dimensions of these spaces are computed.