Related papers: On The Functorialrily Of Stratified Desingularizat…
The original de Rham cohomology due to Souriau and the singular cohomology in diffeology are not isomorphic to each other in general. This manuscript introduces a singular de Rham complex endowed with an integration map into the singular…
We introduce the notion of cofoliation on a stack. A cofoliation is a change of the differentiable structure which amounts to giving a full representable smooth epimorphism. Cofoliations are uniquely determined by their associated Lie…
We say that a complex analytic space, $X$, is an intersection cohomology manifold if and only if the shifted constant sheaf on $X$ is isomorphic to intersection cohomology; this is quickly seen to be equivalent to $X$ being a homology…
A rather simple natural outer derivation of the graded Lie algebra of all vector valued differential forms with the Fr\"olicher-Nijenhuis bracket turns out to be a differential and gives rise to a cohomology of the manifold, which is…
We introduce a space of stable meromorphic differentials with poles of prescribed orders and define its tautological cohomology ring. This space, just as the space of holomorphic differentials, is stratified according to the set of…
We develop a Thom-Mather theory of frontals analogous to Ishikawa's theory of deformations of Legendrian singularities but at the frontal level, avoiding the use of the contact setting. In particular, we define concepts like frontal…
Associated to a differential character is an integral cohomology class, referred to as the characteristic class, and a closed differential form, referred to as the curvature. The characteristic class and curvature are equal in de Rham…
A map between manifolds induces stratifications of both the source and the target according to the occurring multisingularities. In this paper, we study universal expressions-called higher Thom polynomials-that describe the…
There are several compactification procedures in topology, but there is only one standard discretization, namely, replacing the original topology with the discrete topology. We give a notion of discretization which is dual (in categorical…
The initial motivation of this work was to give a topological interpretation of two-periodic twisted de-Rham cohomology which is generalizable to arbitrary coefficients. To this end we develop a sheaf theory in the context of locally…
This is a companion paper our previous submission "\infty-categories monoidales rigides et caracteres de Chern", in which we give a comparison between functions on the derived loop space of a smooth scheme of caracteristic zero, and its…
We construct a functorial pushforward homomorphism in geometric Hodge filtered complex cobordism along proper holomorphic maps between arbitrary complex manifolds. This significantly improves previous results on such transfer maps and is a…
In this note we study umkehr maps in generalized (co)homology theories arising from the Pontrjagin-Thom construction, from integrating along fibers, pushforward homomorphisms, and other similar constructions. We consider the basic…
In casual discussion, a stack is often described as a variety (the coarse space) together with stabilizer groups attached to some of its subvarieties. However, this description does not uniquely specify the stack. Our main result shows that…
In this paper, we define `simplicial GKM orbifold complexes' and study some of their topological properties. We introduce the concept of filtration of regular graphs and `simplicial graph complexes', which have close relations with…
Simplicial presheaves on cartesian spaces provide a general notion of smooth spaces. There is a corresponding smooth version of the singular complex functor, which maps smooth spaces to simplicial sets. We consider the localisation of the…
In the study of equisingularity of families of mappings Gaffney introduced the crucial notion of excellent unfoldings. This definition essentially says that the family can be stratified so that there are no strata of dimension 1 other than…
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…
We initiate the study of the cohomology of (strict polynomial) bifunctors by introducing the foundational formalism, establishing numerous properties in analogy with the cohomology of functors, and providing computational techniques. Since…
This paper presents a gentle introduction to cohomology vanishing theorems, largely based on the paper work of Hongshan Li. It offers an insightful exploration of unitary local systems on complex manifolds, particularly focusing on their…