Related papers: Particle Spaces on Manifolds and Generalized Poinc…
We compare classical and quantum dynamics of a particle in the de Sitter spacetimes with different topologies to show that the result of quantization strongly depends on global properties of a classical system. We present essentially…
In the present paper, we consider several valid notions of orientability of Alexandov spaces and prove that all such conditions are equivalent. Further, we give topological and geometric applications of the orientability. In particular, a…
An analog of the classical Doppler effect is investigated in spaces (manifolds) whose tangent bundle is endowed with a transport along paths, which, in particular, can be parallel one. The obtained results are valid irrespectively to the…
We prove a Poincare-Alexander-Lefschetz duality theorem for rational torus-equivariant cohomology and rational homology manifolds. We allow non-compact and non-orientable spaces. We use this to deduce certain short exact sequences in…
Given a perversity function in the sense of intersection homology theory, the method of intersection spaces assigns to certain oriented stratified spaces cell complexes whose ordinary reduced homology with real coefficients satisfies…
We consider moduli spaces of $d$-dimensional manifolds with embedded particles and discs. In this moduli space, the location of the particles and discs is constrained by the $d$-dimensional manifold. We will compare this moduli space with…
We survey work by the author and Ralf Meyer on equivariant KK-theory. Duality plays a key role in our approach. We organize the survey around the objective of computing a certain homotopy-invariant of a space equipped with a proper action…
We investigate the geometry and topology of compact submanifolds of arbitrary codimension in space forms satisfying a certain pinching condition involving the length of the second fundamental form and the mean curvature. We prove that this…
We consider the class of profinite diffeological spaces, that is, diffeological spaces which diffeologies are deduced by pull-back of diffeologies on finite-dimensional manifolds through a system of projection mappings. This class includes…
A piecewise constant curvature manifold is a triangulated manifold that is assigned a geometry by specifying lengths of edges and stipulating that for a chosen background geometry (Euclidean, hyperbolic, or spherical), each simplex has an…
We reformulate the inequalities among self-closeness numbers of spaces in cofibrations making use of homology dimension and show that the self-closeness number of a space is less than or equal to the homology dimension of the space. Then we…
We introduce a notion of duality for a Lie-Rinehart algebra giving certain bilinear pairings in its cohomology generalizing the usual notions of Poincar\'e duality in Lie algebra cohomology and de Rham cohomology. We show that the duality…
Free Maxwell theory on general four-manifolds may, under certain conditions on the background geometry, exhibit holomorphic factorization in its partition function. We show that when this occurs, new discrete symmetries emerge at orbifold…
The primary objects of study in information geometry are statistical manifolds, which are parametrized families of probability measures, induced with the Fisher-Rao metric and a pair of torsion-free conjugate connections. In recent work,…
We study the compactly supported rational cohomology of configuration spaces of points on wedges of spheres, equipped with natural actions of the symmetric group and the group $Out(F_g)$ of outer automorphisms of the free group. These…
Let $\pi$ be a group satisfying the Farrell-Jones conjecture and assume that $B\pi$ is a 4-dimensional Poincar\'e duality space. We consider topological, closed, connected manifolds with fundamental group $\pi$ whose canonical map to $B\pi$…
In [1] we introduced the concept of structured space, which is a topological space that locally resembles some algebraic structures. In [2] we proceeded the study of these spaces, developing two cohomology theories. The aim of this paper is…
Semi-Riemannian manifolds that satisfy (homogeneous) linear differential conditions of arbitrary order on the curvature are analyzed. They include, in particular, the spaces with (higher-order) recurrent curvature, (higher-order) symmetric…
We study a new class of compact orientable manifolds, called big polygon spaces. They are intersections of real quadrics and related to polygon spaces, which appear as their fixed point set under a canonical torus action. What makes big…
We present an intrinsic geometric classification of the supermanifold of maps from $\mathbb{R}^{0|2}$ to any smooth manifold $S$, avoiding auxiliary structures. The key isomorphism relates this space to the pullback of the decomposable…