Related papers: The Tangle Hypothesis: Dimension 1

We extend the duality theory for topological groups from the classical theory for compact Lie groups, via the topological study by J. R. Klein [Kl01] and the p-complete study for p-compact groups by T. Bauer [Ba04], to a general duality…

In the presence of a nonzero B-field, the symmetries of the $\mathrm E_8\times \mathrm E_8$ heterotic string form a 2-group, or a categorified group, as do the symmetries of the CHL string. We express the bordism groups of the corresponding…

The infinitesimal counterpart of a Lie groupoid is its Lie algebroid. As a vector bundle, it is given by the source vertical tangent bundle restricted to the identity bisection. Its sections can be identified with the invariant vector…

We study two classes of morphisms in infinite type: tamely presented morphisms and morphisms with coherent pullback. These are generalizations of finitely presented morphisms and morphisms of finite Tor-dimension, respectively. The class of…

We state Asymptotic Expansion and Growth Rate conjectures for the Witten-Reshetikhin-Turaev invariants of arbitrary framed links in 3-manifolds, and we prove these conjectures for the natural links in mapping tori of finite-order…

An equivariant Thom isomorphism theorem in operator K-theory is formulated and proven for infinite rank Euclidean vector bundles over finite dimensional Riemannian manifolds. The main ingredient in the argument is the construction of a…

We classify all closed, aspherical Riemannian manifolds M whose universal cover has indiscrete isometry group. One sample application is the theorem that any such M with word-hyperbolic fundamental group must be isometric to a negatively…

A classical theorem due to Quillen (1969) identifies the unitary bordism ring with the Lazard ring, which classifies the universal one-dimensional commutative formal group law. We prove an equivariant generalization of this result by…

We generalize Franz' independence in tensor categories with inclusions from two morphisms (which represent generalized random variables) to arbitrary ordered families of morphisms. We will see that this only works consistently if the unit…

This paper is devoted to the study of the gluing construction for perverse sheaves on $G/U$ introduced by Kazhdan and Laumon ($G$ is a semisimple gourp, $U$ is the unipotent radical of a Borel subgroup in $G$). Kazhdan and Laumon…

We define a subcategory of the category of diffeological spaces, which contains smooth manifolds, the diffeomorphism subgroups and its coadjoint orbits. In these spaces we construct a tangent bundle, vector fields and a de Rham cohomology.

B\"okstedt and Madsen defined an infinite loop map from the embedded $d$-dimensional cobordism category of Galatius, Madsen, Tillmann and Weiss to the algebraic $K$-theory of $BO(d)$ in the sense of Waldhausen. The purpose of this paper is…

We construct higher categories of iterated spans, possibly equipped with extra structure in the form of "local systems", and classify their fully dualizable objects. By the Cobordism Hypothesis, these give rise to framed topological quantum…

We give a new proof of an index theorem for fiber bundles of compact topological manifolds due to Dwyer, Weiss, and Williams, which asserts that the parametrized $A$-theory characteristic of such a fiber bundle factors canonically through…

The double ramification (DR) cycle associated to a line bundle on a family of curves detects where the line bundle becomes fibrewise-trivial. The Hodge-DR Conjecture proposes a formula for powers of the first Chern class of a natural line…

Let $f$ be a continuous ring endomorphism of $\mathbf{Z}_p[[x]]/\mathbf{Z}_p$ of degree $p.$ We prove that if $f$ acts on the tangent space at $0$ by a uniformizer and commutes with an automorphism of infinite order, then it is necessarily…

Let $n$ be a positive even integer and $d$ a positive integer . To every complete family $Z$ of n dimensional degree d hypersurfaces in the projective space with isolated A-D-E singularities we construct according to an idea of…

In this short note, we classify linear categorified open topological field theories in dimension two by pivotal Grothendieck-Verdier categories, a type of monoidal category equipped with a weak, not necessarily rigid duality. In combination…

This paper studies the homotopy theory of parameterized spectrum objects in a model category from a global point of view. More precisely, for a model category $\mathcal{M}$ satisfying suitable conditions, we construct a relative model…

We prove a conjecture of Freed and Hopkins, which relates deformation classes of reflection positive, invertible, $d$-dimensional extended field theories with fixed symmetry type to a certain generalized cohomology of a Thom spectrum. Along…