Related papers: A note on adjunction spaces and G-ANE's

In combinatorial problems it is sometimes possible to define a $G$-equivariant mapping from a space $X$ of configurations of a system to a Euclidean space $\mathbb{R}^m$ for which a coincidence of the image of this mapping with an…

Let $T$ be a compact torus and $(M,\omega)$ a Hamiltonian $T$-space. We give a new proof of the $K$-theoretic analogue of the Kirwan surjectivity theorem in symplectic geometry by using the equivariant version of the Kirwan map introduced…

This note is motivated by recent studies by Eriksson-Bique and Soultanis about the construction of charts in general metric measure spaces. We analyze their construction and provide an alternative and simpler proof of the fact that these…

Equivariant $\Gamma$-spaces model equivariant infinite loop spaces. In this article, we show that there exists a connective Quillen equivalence between the category of equivariant $\Gamma$-spaces and the category of orthogonal spectra.

The purpose of this article is proving the equality of two natural $\mathcal L$-invariants attached to the adjoint representation of a weigth one cusp form, each defined by purely analytic, respectively algebraic means. The proof departs…

Motivated by the analysis and geometry of metric-measure structures in infinite dimensions, we study the category of extended metric-topological spaces, along with many of its distinguished subcategories (such as the one of compact spaces).…

Let G be a $p$-adic Lie group. We develop a dimension theory for coadmissible G-equivariant $\mathcal{D}$-modules on smooth rigid analytic spaces. We introduce the category of weakly holonomic G-equivariant $\mathcal{D}$-modules, study its…

We give a new proof of a theorem of Giordano, Putnam and Skau characterizing orbit equivalence of minimal homeomorphisms of the Cantor space in terms of their sets of invariant Borel probability measures. The proof is based on a…

Let K be an algebraically closed field of characteristic zero, G_m=(K\{0},*) be its multiplicative group, and G_a=(K,+) be its additive group. Consider a commutative linear algebraic group G=G_m^r\times G_a. We study equivariant…

Our work over the past years shows that not only the collection of (for instance) all topological spaces gives rise to a category, but also each topological space can be seen individually as a category by interpreting the convergence…

We develop the theory of categories of measurable fields of Hilbert spaces and bounded fields of bounded operators. We examine classes of functors and natural transformations with good measure theoretic properties, providing in the end a…

We show that quasi-minimizers of non-homogeneous energy functionals on metric measure spaces are locally H\"older continuous and satisfy the Harnack inequality. We assume that the spaces are doubling and support a Poincar\'e inequality. The…

This short survey reviews some aspects of spaces of positive-definite self-adjoint linear transformations on R^n and on C^n, including the standard Riemannian metric and the relation with the exponential mapping acting on self-adjoint…

We prove a result about partitioning an absolute continuous measure in $\mathbb R^d$ into 2d equal parts by a system of cones with common vertex, where $d$ is an odd prime power. The proof is topological and based on the calculation of the…

Following an idea close to one given by C. G. Torre (private communication), we prove that Riemannian spaces (M,g) and (M,h) that are related by a Gurses type (b) transformation [M. Gurses, Phys. Rev. Lett. 70, 367 (1993)] or, equivalently,…

The quantum lens spaces form a natural and well-studied class of noncommutative spaces which can be subjected to classification using algebraic invariants by drawing on the fully developed classification theory of unital graph…

We construct rational models for classifying spaces of self-equivalences of bundles over simply connected finite CW-complexes relative to a given simply connected subcomplex. Via work of Berglund-Madsen and Krannich this specializes to…

Many recent researches indicate that several gravitational D-dimensional theories suitably coupled to some matter fields (including in particular pure gravity in D dimensions, the low energy effective actions of the bosonic string and the…

In this research article, we formulate and prove multidimensional Widder--Arendt theorem and integrated form of multidimensional Widder--Arendt theorem for functions with values in sequentially complete locally convex spaces. Established…

In a strengthening of the G-Signature Theorem of Atiyah and Singer, we compute, at least in principle (modulo certain torsion of exponent dividing a power of the order of G), the class in equivariant K-homology of the signature operator on…