Related papers: Khovanov homotopy types and the Dold-Thom functor

We develop a space-level formulation of Khovanov skein homology by constructing a stable homotopy type for annular links. We explicitly define a cover functor from the skein flow category to the cube flow category, thereby establishing the…

Dold-Thom functors are generalizations of infinite symmetric products, where integer multiplicities of points are replaced by composable elements of a partial abelian monoid. It is well-known that for any connective homology theory, the…

Given an $m$-periodic link $L\subset S^3$, we show that the Khovanov spectrum $\mathcal{X}_L$ constructed by Lipshitz and Sarkar admits a homology group action. We relate the Borel cohomology of $\mathcal{X}_L$ to the equivariant Khovanov…

In this paper, we discuss two topics: first, we show how to convert 1+1-topological quantum field theories valued in symmetric bimonoidal categories into stable homotopical data, using a machinery by Elmendorf and Mandell. Then, we discuss,…

We prove that the spectrum constructed by Gonz\'alez-Meneses, Manch\'on and the second author is stably homotopy equivalent to the Khovanov spectrum of Lipshitz and Sarkar at its extreme quantum grading.

We prove that the Khovanov spectra associated to links and tangles are functorial up to homotopy and sign.

The purpose of this note is to point out that simplicial methods and the well-known Dold-Kan construction in simplicial homotopy theory can be fruitfully applied to convert link homology theories into homotopy theories. Dold and Kan prove…

We introduce a functor from the cube to the Burnside 2-category and prove that it is equivalent to the Khovanov spectrum given by Lipshitz and Sarkar in the almost-extreme quantum grading. We provide a decomposition of this functor into…

In this paper, we give a new construction of a Khovanov homotopy type. We show that this construction gives a space stably homotopy equivalent to the Khovanov homotopy types constructed in [LS14a] and [HKK] and, as a corollary, that those…

This paper contains a complete computation of the homotopy ring of the spectrum of topological modular forms constructed by Hopkins and Miller. The computation is done away from 6, and at the (interesting) primes 2 and 3 separately, and in…

In this paper, we prove an equivariant version of the classical Dold-Thom theorem. Associated to a finite group, a CW-complex on which this group acts and a covariant coefficient system in the sense of Bredon, we functorially construct a…

Let $G$ be a finite group. For a based $G$-space $X$ and a Mackey functor $M$, a topological Mackey functor $X\widetilde\otimes M$ is constructed, which will be called the stable equivariant abelianization of $X$ with coefficients in $M$.…

We investigate group actions on homotopy coherent diagrams. This is used to prove an equivalence between realizations of equivariant cubical flow categories and external actions on Burnside functors. In particular, the results imply that…

We obtain combinatorial model categories of parametrised spectra, together with systems of base change Quillen adjunctions associated to maps of parameter spaces. We work with simplicial objects and use Hovey's sequential and symmetric…

A functor on compact Hausdorf spaces is constructed as the sum of certain equivariant K-theory groups. It is shown that the functor takes values in lambda-rings and satisfies a Thom isomorphism. In the case that the space is a CW-complex…

We define a Khovanov-Lipshitz-Sarkar stable homotopy type for the homotopical Khovanov homology of links in the thickened torus after the authors introduced that in the case of higher genus surfaces in the previous paper of this one.

This note extends Quillen's Theorem A to a large class of categories internal to topological spaces. This allows us to show that under a mild condition a fully faithful and essentially surjective functor between such topological categories…

The Blanchet link homology theory is an oriented model of Khovanov homology, functorial over the integers with respect to link cobordisms. We formulate a stable homotopy refinement of the Blanchet theory, based on a comparison of the…

We prove that the $G$-equivariant mod $p$ Eilenberg--MacLane spectrum arises as an equivariant Thom spectrum for any finite, $p$-power cyclic group $G$, generalizing a result of Behrens and the second author in the case of the group $C_2$.…

We investigate implications of an old conjecture in unstable homotopy theory related to the Cohen-Moore-Neisendorfer theorem and a conjecture about the $\mathbf{E}_{2}$-topological Hochschild cohomology of certain Thom spectra (denoted $A$,…