Related papers: An $\mathsf{A}_{\infty}$ version of the Poincar\'e…

In the present paper the cyclic homology functor from the category of $A_\infty$-algebras over any commutative unital ring $K$ to the category of graded $K$-modules is constructed. Further, it is showed that this functor sends homotopy…

We introduce the notion of balanced pair of additive subcategories in an abelian category. We give sufficient conditions under which the balanced pair of subcategories gives rise to equivalent homotopy categories of complexes. As an…

The analytic continuation to an imaginary velocity $i\xi$ of the canonical partition function of a thermal system expressed in a moving frame has a natural implementation in the Euclidean path-integral formulation in terms of shifted…

Let $G$ be a discrete group. The topological category of finite dimensional unitary representations of $G$ is symmetric monoidal under direct sum and has an associated $\mathbb{E}_\infty$-space $\mathcal{K}^{\mathrm{def}}(G)$. We show that…

We show that several apparently unrelated formulas involving left or right Bousfield localizations in homotopy theory are induced by comparison maps associated with pairs of adjoint functors. Such comparison maps are used in the article to…

We prove a fractional version of Poincar\'e inequalities in the context of $\R^n$ endowed with a fairly general measure. Namely we prove a control of an $L^2$ norm by a non local quantity, which plays the role of the gradient in the…

We introduce and study the notion of \emph{equivariant homotopic distance} $D_G(f,g)$ between $G$-maps $f,g \colon X \to Y$. We show that the equivariant Lusternik-Schnirelmann category and the equivariant topological complexity are…

Given a smooth scheme over $\Z/p^n\Z$ with a lift of relative Frobenius to $\Z/p^{n+1}\Z$, we construct a functor from the category of Higgs modules to that of modules with integrable connections as the composite of the level raising…

For a complex reductive group $G$, we prove a homological mirror symmetry between the wrapped Fukaya category of the affine Toda system for $G$ and coherent sheaves on the regular centralizer group scheme for the Langlands dual group…

We define a space of relative embedded thickenings of a given map from a finite complex to a Poincare Duality space, and show that there is a highly connected stabilization map between such spaces induced by fiberwise suspension. As a…

We use Almgren's framework of multi-valued maps to construct a multi-valued inverse $F:f(\Omega)\to \mathcal A_d(\mathbb R^n)$ of a quasiregular map $f:\Omega\to \mathbb R^n$ of finite degree $d$. We then develop a pull-back theory of…

Let $F$ be a local non archimedian field of characteristic $0$, and $G$ a non-connected reductive group over $F$. We denote $G^0$ the connected component of the identity and assume the quotient $G/G^0$ is abelian. For $f$ a locally constant…

We prove that an \'etale fibration between $L_\infty$-bundles admits local sections composed of several elementary morphisms of particularly simple and accessible type. As applications, we establish an inverse function theorem for…

We show that if G is a finite constant group acting on a scheme X such that the order of G is invertible in the residue fields of X, then the G-equivariant motivic stable homotopy category of X is equivalent to the stabilization of the…

Let X be a compact connected Riemann surface. Fix a positive integer r and two nonnegative integers d_p and d_z. Consider all pairs of the form (F, f), where F is a holomorphic vector bundle on X of rank r and degree d_z-d_p, and f :…

The notion of Hochschild cochains induces an assignment from $Aff$, affine DG schemes, to monoidal DG categories. We show that this assignment extends, under some appropriate finiteness conditions, to a functor $\mathbb H: Aff \to…

Using the microlocal theory of sheaves, we associate a category to each Weinstein manifold. By constructing a microlocal specialization functor, we show that exact Lagrangians give objects in our category, and that the category is invariant…

We extend the theory of diffeomorphism-invariant spin network states from the real-analytic category to the smooth category. Suppose that G is a compact connected semisimple Lie group and P -> M is a smooth principal G-bundle. A `cylinder…

To any non-negatively graded dg Lie algebra $g$ over a field $k$ of characteristic zero we assign a functor $\Sigma_g: art/k \to Kan$ from the category of commutative local artinian $k$-algebras with the residue field $k$ to the category of…

Given a natural number $m$ and a log smooth integral morphism $X\to S$ of fine log schemes of characteristic $p>0$ with a lifting of its Frobenius pull-back $X'\to S$ modulo $p^{2}$, we use indexed algebras ${\cal A}_{X}^{gp}$, ${\cal…