Related papers: A looping-delooping adjunction for topological spa…

This paper gives a uniform-theoretic refinement of classical homotopy theory. Both cubical sets (with connections) and uniform spaces admit classes of weak equivalences, special cases of classical weak equivalences, appropriate for the…

For a weak 2-group, we construct a bicategory of flat 2-group bundles over differentiable stacks as a localization of a functor bicategory. This description is amenable to explicit geometric constructions. For example, we show that flat…

The configuration space of k points on a manifold carries an action of its diffeomorphism group. The homotopy quotient of this action is equivalent to the classifying space of diffeomorphisms of a punctured manifold, and therefore admits…

We show that the notions of homotopy epimorphism and homological epimorphism in the category of differential graded algebras are equivalent. As an application we obtain a characterization of acyclic maps of topological spaces in terms of…

For a topological group $G$ let $E_{\textsf{com}}(G)$ be the total space of the universal transitionally commutative principal $G$-bundle as defined by Adem--Cohen--Torres-Giese. So far this space has been most studied in the case of…

This paper focuses on the study of a new category of vector bundles. The objects of this category, called chiral vector bundles, are pairs given by a complex vector bundle along with one of its automorphisms. We provide a classification for…

This paper continues the author's program to investigate the question of when a homotopy of 2-cocycles $\Omega = \{\omega_t\}_{t \in [0,1]}$ on a locally compact Hausdorff groupoid $\mathcal{G}$ induces an isomorphism of the $K$-theory…

From every pair of adjoint functors it is possible to produce a (possibly trivial) equivalence of categories by restricting to the subcategories where the unit and counit are isomorphisms. If we do this for the adjunction between effect…

This paper explores the relationship amongst the various simplicial and pseudo-simplicial objects characteristically associated to any bicategory C. It proves the fact that the geometric realizations of all of these possible candidate…

For a semisimple complex algebraic group $G$ we determine the rational cohomology and the Hodge-Tate structure of the moduli stack ${\mathscr B}un_{G,X}$ of principal $G$-bundles over a connected smooth complex projective variety $X$ of…

Let $F$ be a local field with residue field $k$. The classifying space of $GL_n(F)$ comes canonically equipped with a map to the delooping of the $K$-theory space of $k$. Passing to loop spaces, such a map abstractly encodes a homotopy…

A covariant functor from the category of mapping tori to a category of AF-algebras is constructed; the functor takes continuous maps between such manifolds to stable homomorphisms between the corresponding AF-algebras. We use this functor…

The aim of section 1 is to define the homotopic functor to category of Abelian groups, connected with the special classes of bundles with fiber matrix algebra or projective space. The aim of section 2 is to define some generalization of the…

The relationship between associative composition algebras of dimensions 2 and 4 within the context of homogeneous spaces, with a particular focus on Hamiltonian quaternions, is explored. In the special case of Hamiltonian quaternions, the…

For analyzing stationary Yang-Mills connections in higher dimensions, one has to work with Morrey-Sobolev bundles and connections. The transition maps for a Morrey-Sobolev principal $G$-bundles are not continuous and thus the usual notion…

We define the notion of a trace kernel on a manifold M. Roughly speaking, it is a sheaf on M x M for which the formalism of Hochschild homology applies. We associate a microlocal Euler class to such a kernel, a cohomology class with values…

Let $G$ be a compact connected Lie group with $\pi_1(G)\cong\mathbb{Z}$. We study the homotopy types of gauge groups of principal $G$-bundles over Riemann surfaces. This can be applied to an explicit computation of the homotopy groups of…

We construct cohomology classes in the space of knots by considering a bundle over this space and "integrating along the fiber" classes coming from the cohomology of configuration spaces using a Pontrjagin-Thom construction. The bundle we…

We construct a motivic homotopy theory for rigid analytic varieties with the rigid analytic affine line $\mathbb{A} ^1_\mathrm{rig}$ as an interval object. This motivic homotopy theory is inspired from, but not equal to, Ayoub's motivic…

Recently twisted K-theory has received much attention due to its applications in string theory and the announced result by Freed, Hopkins and Telemann relating the twisted equivariant K-theory of a compact Lie group to its Verlinde algebra.…