Related papers: Higher rho-invariants and the surgery structure se…

Let X be a Noetherian scheme of finite dimension and denote by rho the (additive inverse of the) morphism in SH(X) from S to Gm corresponding to the unit -1. Here SH(X) denotes the motivic stable homotopy category. We show that the category…

We prove a rigidity property for mapping tori associated to minimal topological dynamical systems using tools from noncommutative geometry. More precisely, we show that under mild geometric assumptions, an orientation-preserving leafwise…

We show that shift equivalence of essential adjacency matrices coincides with gauge-equivariant homotopy equivalence of their stabilized graph C*-algebras. This provide the first equivalent formulation of shift equivalence of essential…

We study K-theory classes of Hamiltonian loop group spaces represented by admissible Fredholm complexes. We prove various equivariant index formulae in this context. In a sequel to this article we show that, when specialized to a family of…

Using a homological invariant together with an obstruction class in a certain Ext^2-group, we may classify objects in triangulated categories that have projective resolutions of length two. This invariant gives strong classification results…

In the context of categories equipped with a structure of nullhomotopies, we introduce the notion of homotopy torsion theory. As special cases, we recover pretorsion theories as well as torsion theories in multi-pointed categories and in…

These notes illustrates the power of formulating ideas of commutative algebra in a homotopy invariant form. They can then be applied to derived categories of rings or ring spectra. These ideas are powerful in classical algebra, in…

We establish compatibility of Lie structures that appear in homotopy calculus of functors and isotopy calculus of embeddings. On one hand, we give a new proof of the Johnson--Arone--Mahowald result describing the layers of the Goodwillie…

We classify hypersurfaces with rotational symmetry and positive constant $r$-th mean curvature in $\mathbb H^n \times \mathbb R$. Specific constant higher order mean curvature hypersurfaces invariant under hyperbolic translation are also…

Chiral higher spin gravity is defined in terms of a strong homotopy algebra of pre-Calabi-Yau type (noncommutative Poisson structure). All structure maps are given by the integrals over the configuration space of concave polygons and the…

We prove index formulas for elliptic operators acting between sections of C*-vector bundles on a closed manifold. The formulas involve Karoubi's Chern character from K-theory of a C*-algebra to de Rham homology of smooth subalgebras. We…

We prove the Riemann-Roch theorem for homotopy invariant $K$-theory and projective local complete intersection morphisms between finite dimensional noetherian schemes, without smoothness assumptions. We also prove a new Riemann-Roch theorem…

Exploiting the graph product structure and results concerning amalgamated free products of C*-algebras we provide an explicit computation of the K-theoretic invariants of right-angled Hecke C*-algebras, including concrete algebraic…

We show that coarse maps between countable metric spaces of bounded geometry induce natural transformations of sufficiently good endofunctors of C*-algebras and prove that this correspondence is invariant with respect to coarse homotopies.

In this paper, we prove that there is a canonical homotopy $(n+1)$-algebra structure on the shifted operadic deformation complex $Def(e_n\to\mathcal{P})[-n]$ for any operad $\mathcal{P}$ and a map of operads $f\colon e_n\to\mathcal{P}$.…

Equivalence classes of gapped Hamiltonians compatible with given symmetry constraints, such as those underlying topological insulators, can be defined in many ways. For the non-chiral classes modelled by vector bundles over Brillouin tori,…

Groups $\Pi_k(X;\sigma)$ of "flagged homotopies" are introduced of which the usual (abelian for $k>1$) homotopy groups $\pi_k(X;p)$ is the limit case for flags $\sigma$ contracted to a point $p$. Calculus of exterior forms with values in…

Given a group $G$ acting cocompactly on a smooth manifold $M$ by deck transformations, there is an integration map, defined recently by Kato, Kishimoto and Tsutaya, from the top-degree bounded de Rham cohomology of $M$ to the coinvariants…

Let $N$ be a closed spin manifold with positive scalar curvature and $D_N$ the Dirac operator on $N$. Let $M_1$ and $M_2$ be two Galois covers of $N$ such that $M_2$ is a quotient of $M_1$. Then the quotient map from $M_1$ to $M_2$…

In this paper, we introduce a new class of structured spaces which is locally modeled by Costello's L-infinity spaces. This provides an alternative approach to study the derived geometric structures in the algebraic, analytic, or smooth…