Related papers: External Spanier-Whitehead duality and homology re…

A procedure for constructing bivariant theories by means of Grothendieck duality is developed. This produces, in particular, a bivariant theory of Hochschild (co)homology on the category of schemes that are flat, separated and essentially…

We revisit Spakula's uniform K-homology, construct the external product for it and use this to deduce homotopy invariance of uniform K-homology. We define uniform K-theory and on manifolds of bounded geometry we give an interpretation of it…

Starting from the generating functional of the theory of relativistic spinors in 2+1 dimensions interacting through the pure Chern-Simons gauge field, the S-matrix is constructed and seen to be formally the same as that of spinor quantum…

In this paper we take some classical ideas from commutative algebra, mostly ideas involving duality, and apply them in algebraic topology. To accomplish this we interpret properties of ordinary commutative rings in such a way that they can…

We show if $A$ is a finite CW-complex such that algebraic theories detect mapping spaces out of $A$, then $A$ has the homology type of a wedge of spheres of the same dimension. Furthermore, if $A$ is simply connected then $A$ has the…

In this paper one considers three homotopy functors on the category of manifolds, $hH^\ast, cH^\ast, sH^\ast,$ and parallel them with other three homotopy functors on the category of connected commutative differential graded algebras,…

We construct Chern-Simons bundles as $\mathrm{Aut}^{+}P$-equivariant $U(1)$ -bundles with connection over the space of connections $\mathcal{A}_{P}$ on a principal $G$-bundle $P\rightarrow M$. We show that the Chern-Simons bundles are…

For a finite dimensional algebra $A$, we prove that the bounded homotopy category of projective $A$-modules and the bounded derived category of $A$-modules are dual to each other via certain categories of locally-finite cohomological…

Using the superconformal (SC) indices techniques, we construct Seiberg type dualities for $\mathcal{N}=1$ supersymmetric field theories outside the conformal windows. These theories are physically distinguished by the presence of chiral…

For a finite group $G$, there is a map $RO(G) \to {\rm Pic}(Sp^G)$ from the real representation ring of $G$ to the Picard group of $G$-spectra. This map is not known to be surjective in general, but we prove that when $G$ is cyclic this map…

To a digraph with a choice of certain integral basis, we construct a CW complex, whose integral singular cohomology is canonically isomorphic to the path cohomology of the digraph as introduced in \cite{GLMY}. The homotopy type of the CW…

In \cite{FMX19}, it is proved that the convolution algebra of top Borel-Moore homology on Steinberg variety of type $B/C$ realizes $U(sl_n^{\theta})$, where $sl_{n}^{\theta}$ is the fixed point subalgebra of involution on $sl_n$. So top…

We show that $v_n$-periodic homotopy groups detect homotopy equivalences between simply-connected finite CW-complexes.

We show that Shipley's "detection functor" for symmetric spectra generalizes to motivic symmetric spectra. As an application, we construct motivic strict ring spectra representing morphic cohomology, semi-topological $K$-theory, and…

We describe spectral model category structures on the categories of cyclotomic spectra and $p$-cyclotomic spectra (in orthogonal spectra) with triangulated homotopy categories. We show that the functors $TR$ and $TC$ are corepresentable in…

Let $G$ be a finite group acting on a small category $I$. We study functors $X \colon I \to \mathscr{C}$ equipped with families of compatible natural transformations that give a kind of generalized $G$-action on $X$. Such objects are called…

In this paper, we mainly build up the theory of sheaf-correspondence filtered spaces and stratified de Rham complexes for studying singular spaces. We prove the finiteness of a stratified de Rham cohomology and obtain its isomorphism to…

Given a C$^*$-dynamical system $(A, G, \alpha)$ one defines a homomorphism, called the Chern-Connes character, that take an element in $K_0(A) \oplus K_1(A)$, the K-theory groups of the C$^*$-algebra $A$, and maps it into…

The evaluation of Alexander-Spanier cochains over formal simplices in a topological space leads to a notion of integration of Alexander-Spanier cohomology classes over \v{C}ech homology classes. The integral defines an explicit and…

Given a topological modular functor $\mathcal{V}$ in the sense of Walker \cite{Walker}, we construct vector bundles over $\bar{\mathcal{M}}_{g,n}$, whose Chern classes define semi-simple cohomological field theories. This construction…