Results 21 to 30 of about 3,075 (93)

Assembly of constructible factorization algebras

Journal of Topology, Volume 19, Issue 1, March 2026.
Abstract We provide a toolbox of extension, gluing, and assembly techniques for factorization algebras. Using these tools, we fill various gaps in the literature on factorization algebras on stratified manifolds, the main one being that constructible factorization algebras form a sheaf of symmetric monoidal ∞$\infty$‐categories.
Eilind Karlsson, Claudia I. Scheimbauer, Tashi Walde   +2 more
wiley   +1 more source

The localization sequence for the algebraic K-theory of topological K-theory

, 2006
We prove a conjecture of Rognes by establishing a localization cofiber sequence of spectra, K(Z) to K(ku) to K(KU) to Sigma K(Z), for the algebraic K-theory of topological K-theory. We deduce the existence of this sequence as a consequence of a devissage
Andrew J. Blumberg, C. Ausoni, C. Ausoni, J. E. McClure, Michael A. Mandell   +4 more
core   +2 more sources

On an extension of the notion of Reedy category [PDF]

, 2008
We extend the classical notion of a Reedy category so as to allow non-trivial automorphisms. Our extension includes many important examples occuring in topology such as Segal's category Gamma, or the total category of a crossed simplicial group such as ...
Clemens Berger, Ieke Moerdijk, Math Z, Mathematische Zeitschrift   +3 more
core   +6 more sources

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

Adding inverses to diagrams encoding algebraic structures [PDF]

, 2013
We modify a previous result, which showed that certain diagrams of spaces are essentially simplicial monoids, to construct diagrams of spaces which model simplicial groups.
Bergner, Julia E.
core  

Scissors congruence K$K$‐theory for equivariant manifolds

Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.
Abstract We introduce a scissors congruence K$K$‐theory spectrum that lifts the equivariant scissors congruence groups for compact G$G$‐manifolds with boundary, and we show that on π0$\pi _0$, this is the source of a spectrum‐level lift of the Burnside ring‐valued equivariant Euler characteristic of a compact G$G$‐manifold.
Mona Merling, Ming Ng, Julia Semikina, Alba Sendón Blanco, Lucas Williams   +4 more
wiley   +1 more source

On Fico's Lemmata and the homotopy type of certain gyrations

Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.
Abstract We undertake to determine the homotopy type of gyrations of sphere products and of connected sums, thereby generalising results known in earlier literature as ‘Fico's Lemmata’ which underpin gyrations in their original formulation from geometric topology.
Sebastian Chenery
wiley   +1 more source

Diagram spaces, diagram spectra, and spectra of units

, 2012
This article compares the infinite loop spaces associated to symmetric spectra, orthogonal spectra, and EKMM S-modules. Each of these categories of structured spectra has a corresponding category of structured spaces that receives the infinite loop space
Elmendorf, Hovey, John A Lind, Lewis, Mandell, May, May, May, Schlichtkrull, Shulman   +9 more
core   +1 more source

Modeling (∞,1)$(\infty,1)$‐categories with Segal spaces

Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.
Abstract In this paper, we construct a model structure for (∞,1)$(\infty,1)$‐categories on the category of simplicial spaces, whose fibrant objects are the Segal spaces. In particular, we show that it is Quillen equivalent to the models of (∞,1)$(\infty,1)$‐categories given by complete Segal spaces and Segal categories.
Lyne Moser, Joost Nuiten
wiley   +1 more source

The accessibility rank of weak equivalences [PDF]

, 2015
We study the accessibility properties of trivial cofibrations and weak equivalences in a combinatorial model category and prove an estimate for the accessibility rank of weak equivalences.
Raptis, G., Rosický, J.
core