Algebraic Topology Papers of the Week

We prove the Díaz$\unicode[Arial]{x2013}$Park conjecture for sharpness of saturated fusion systems.

By introducing the notion of stable compatibility, we provide a framework in the model category theory which addresses the existence of a stable model structure on the category of modules over a monad.

We prove Lurie's proposed description of left rigid symmetric monoidal $(\infty,n)$-categories in terms of purely $\infty$-categorical data.

We present two geometric applications of heat flow methods on the discrete hypercube { - 1 , 1 } n .

In this paper, we introduce the landscape interval, a subset of the parameter space of a multiparameter persistence module which records changes in the rank function in all directions simultaneously.

In this article, we introduce Borel--Moore and uniformly finite versions of magnitude homology and path homology for locally finite graphs by allowing possibly infinite chains subject to local finiteness and boundedness conditions.

For a quiver $Q$, we introduce and study $Q$-operads (or operads over $Q$), defined as a special sort of $\mathbf{fc}$-multicategories or virtual double categories, in which the directions of the arrows of $Q$ encode the permitted input orderings.

We obtain new constraints on the topology of Lagrangian submanifolds in the standard symplectic vector space $\mathbb{C}^n$ using Floer theory on the based loop space, generalizing a theorem of Fukaya-Irie.

We show that $f$ is a convex embedding if and only if every shade is contractible.

We provide a novel, homotopy theoretic model for the motivic Eilenberg--Mac Lane spaces $K(Z_{(p)}(n), 2n) \in Spc(k)$ over fields of characteristic p. Using this, we determine their motives and, consequently, determine the motivic Steenrod algebra at the characteristic.

Abstract. We study a probabilistic variant of the [Formula: see text]th sequential parametrized topological complexity, which bounds this classical invariant from below and measures the difficulty in constructing permissive parametrized motion planning algorithms.

In this paper, we establish a topological classification of Bazaikin spaces whose sixth cohomology groups have orders prime to \(5\).

We construct a cohomology theory $H_A(-)$ canonically attached to any 1-dimensional commutative group scheme A over a connective $E_\infty$-ring.

For any odd prime number $p$, we solve the topological period-index problem for a $p$-primary element of the Brauer group of a CW-complex of dimension not greater than $2p+2$.

We construct an explicit small model for the $\infty$-groupoid of null-concordances of higher gauge curvatures by algorithmically trivializing their nonlinear Bianchi identities.

We study the tensor triangular geometry of derived categories of valuation domains, obtaining complete ring-theoretic characterizations of their main structural properties.

We prove that if a smooth Fano variety $X$ has the same dimension and Picard number as $F$, then the existence of a continuous map $X\to F$ of odd topological degree implies $X$ is isomorphic to $F$.

We give a direct and explicit construction of the homotopy span model of linear logic originally formulated by Melliès using abstract homotopy theory in the Quillen category Cat of small categories equipped with its natural model structure.

Aguiar, Bergeron, and Sottile showed that the coalgebra of quasisymmetric functions is terminal among connected graded coalgebras with a zeta function. After developing the notions of gradings and zeta functions for decomposition spaces, we establish an objective homotopic version of this result.

In this paper we determine which combinations of partition functions can be isolated from the non-universal factors.