Results 21 to 30 of about 50 (45)

Obstructions to homotopy invariance of loop coproduct via parameterized fixed‐point theory

Journal of Topology, Volume 19, Issue 1, March 2026.
Abstract Given f:M→N$f:M \rightarrow N$ a homotopy equivalence of compact manifolds with boundary, we use a construction of Geoghegan and Nicas to define its Reidemeister trace [T]∈π1st(LN,N)$[T] \in \pi _1^{st}(\mathcal {L}N, N)$. We realize the Goresky–Hingston coproduct as a map of spectra, and show that the failure of f$f$ to entwine the spectral ...
Lea Kenigsberg, Noah Porcelli
wiley   +1 more source

The Picard group in equivariant homotopy theory via stable module categories

Journal of Topology, Volume 18, Issue 2, June 2025.
Abstract We develop a mechanism of “isotropy separation for compact objects” that explicitly describes an invertible G$G$‐spectrum through its collection of geometric fixed points and gluing data located in certain variants of the stable module category.
Achim Krause
wiley   +1 more source

Fundamental groups of clique complexes of random graphs

Transactions of the London Mathematical Society, Volume 2, Issue 1, Page 1-32, 2015., 2015
We study fundamental groups of clique complexes associated to random Erdős–Rényi graphs Γ. We establish thresholds for a number of properties of fundamental groups of these complexes XΓ. In particular, if p=nα, then we show that gdim(π1(XΓ))=cd(π1(XΓ))=1ifα<−12,gdim(π1(XΓ))=cd(π1(XΓ))=2if−12<α<−1130,gdim(π1(XΓ))=cd(π1(XΓ))=∞if−1130<α<−13 ...
Armindo Costa, Michael Farber, Danijela Horak   +2 more
wiley   +1 more source

Assouad–Nagata dimension of minor‐closed metrics

Proceedings of the London Mathematical Society, Volume 130, Issue 3, March 2025.
Abstract Assouad–Nagata dimension addresses both large‐ and small‐scale behaviors of metric spaces and is a refinement of Gromov's asymptotic dimension. A metric space M$M$ is a minor‐closed metric if there exists an (edge‐)weighted graph G$G$ satisfying a fixed minor‐closed property such that the underlying space of M$M$ is the vertex‐set of G$G$, and
Chun‐Hung Liu
wiley   +1 more source

The Mumford conjecture (after Bianchi)

Journal of Topology, Volume 18, Issue 1, March 2025.
Abstract We give a self‐contained and streamlined rendition of Andrea Bianchi's recent proof of the Mumford conjecture using moduli spaces of branched covers.
Ronno Das, Dan Petersen
wiley   +1 more source

A stable splitting of factorisation homology of generalised surfaces

Journal of the London Mathematical Society, Volume 111, Issue 2, February 2025.
Abstract For a manifold W$W$ and an Ed$\smash{E_{\smash{d}} }$‐algebra A$A$, the factorisation homology ∫WA$\smash{\int _W A}$ can be seen as a generalisation of the classical configuration space of labelled particles in W$W$. It carries an action by the diffeomorphism group Diff∂(W)$\mathrm{Diff}{}_\partial (W)$, and for the generalised surfaces Wg,1≔(
Florian Kranhold
wiley   +1 more source

The slice spectral sequence for a motivic analogue of the connective K(1)$K(1)$‐local sphere

Proceedings of the London Mathematical Society, Volume 129, Issue 5, November 2024.
Abstract We compute the 2‐adic effective slice spectral sequence (ESSS) for the motivic stable homotopy groups of L$L$, a motivic analogue of the connective K(1)$K(1)$‐local sphere over prime fields of characteristic not two. Together with the analogous computation over algebraically closed fields, this yields information about the motivic K(1)$K(1 ...
Hana Jia Kong, J. D. Quigley
wiley   +1 more source

Some rational homology computations for diffeomorphisms of odd‐dimensional manifolds

Journal of Topology, Volume 17, Issue 1, March 2024.
Abstract We calculate the rational cohomology of the classifying space of the diffeomorphism group of the manifolds Ug,1n:=#g(Sn×Sn+1)∖int(D2n+1)$U_{g,1}^n:= \#^g(S^n \times S^{n+1})\setminus \mathrm{int}(D^{2n+1})$, for large g$g$ and n$n$, up to degree n−3$n-3$.
Johannes Ebert, Jens Reinhold
wiley   +1 more source

Stable homotopy groups of spheres. [PDF]

Proc Natl Acad Sci U S A, 2020
Isaksen DC, Wang G, Xu Z.
europepmc   +1 more source

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On set-star-$K$-Hurewicz spaces

Bulletin of the Belgian Mathematical Society - Simon Stevin, 2022
Sumit Singh
exaly