Related papers: A Diffeological Construction of Singer's Universal…
Given a two--dimensional mapping $U$ whose components solve a divergence structure elliptic equation, we give necessary and sufficient conditions on the boundary so that $U$ is a global diffeomorphism.
By making use of Halperin's local systems over simplicial sets and the model structure of the category of diffeological spaces due to Kihara, we introduce a framework of rational homotopy theory for such smooth spaces with arbitrary…
We introduce a singular chain intersection homology theory which generalizes that of King and which agrees with the Deligne sheaf intersection homology of Goresky and MacPherson on any topological stratified pseudomanifold, compact or not,…
We consider the moduli space of flat $SO(2n+1)$-connections (up to gauge transformations) on a Riemann surface, with fixed holonomy around a marked point. There are natural line bundles over this moduli space; we construct geometric…
Tangent categories are categories equipped with a tangent functor: an endofunctor with certain natural transformations which make it behave like the tangent bundle functor on the category of smooth manifolds. They provide an abstract…
This paper develops the theory of a sheaf of normal differential operators to a submanifold Y of a complex manifold X as a generalization of the normal bundle. We show that the global sections of this sheaf play an analogous role for formal…
The existence of a model structure on the category $\mathcal{D}$ of diffeological spaces is crucial to developing smooth homotopy theory. We construct a compactly generated model structure on the category $\mathcal{D}$ whose weak…
We consider geometric and analytical aspects of M-theory on a manifold with boundary Y. The partition function of the C-field requires summing over harmonic forms. When Y is closed Hodge theory gives a unique harmonic form in each de Rham…
We present a pair of smooth fiber bundles over the circle with a common $4$-dimensional fiber with the following properties: (1) their total spaces are diffeomorphic to each other; (2) they are isomorphic to each other as topological fiber…
Knots naturally appear in continuous dynamical systems as flow periodic trajectories. However, discrete dynamical systems are also closely connected with the theory of knots and links. For example, for Pixton diffeomorphisms, the…
We consider the connected sum of two three-dimensional lens spaces $L_1\#L_2$, where $L_1$ and $L_2$ are non-diffeomorphic and are of a certain "generic" type. Our main result is the calculation of the cohomology ring…
We study the relationship between many natural conditions that one can put on a diffeological vector space: being fine or projective, having enough smooth (or smooth linear) functionals to separate points, having a diffeology determined by…
The theory of intersection spaces assigns cell complexes to certain stratified topological pseudomanifolds depending on a perversity function in the sense of intersection homology. The main property of the intersection spaces is Poincar\'e…
In this paper we give a complete topological classification of orientation preserving Morse-Smale diffeomorphisms on orientable closed surfaces. For MS diffeomorphisms with relatively simple behaviour it was known that such a classification…
This paper establishes an equivalence between two distinct frameworks for constructing and relating smooth manifolds: the geometric theory of \emph{$\star$-diagrams} and the string-theory-inspired notion of \emph{spherical T-duality}. We…
We establish that Hitchin's connection exist for any rigid holomorphic family of Kahler structures on any compact pre-quantizable symplectic manifold which satisfies certain simple topological constraints. Using Toeplitz operators we prove…
Wehrheim and Woodward have shown how to embed all the canonical relations between symplectic manifolds into a category in which the composition is the usual one when transversality and embedding assumptions are satisfied. A morphism in…
We study how the notion of tangent space can be extended from smooth manifolds to diffeological spaces, which are generalizations of smooth manifolds that include singular spaces and infinite-dimensional spaces. We focus on two definitions.…
We construct a multiplicative spectral sequence converging to the symplectic cohomology ring of any affine variety $X$, with first page built out of topological invariants associated to strata of any fixed normal crossings compactification…
Directed Algebraic Topology is beginning to emerge from various applications. The basic structure we shall use for such a theory, a 'd-space', is a topological space equipped with a family of 'directed paths', closed under some operations.…