Results 31 to 40 of about 3,365 (87)

The Cofibre of the Transfer Map [PDF]

Proceedings of the American Mathematical Society, 1985
The transfer for a finite covering \(p: X\to B\) is a stable map tr: \(\Sigma\) \({}^ 0B_+\to \Sigma^ 0X_+\). Let \({\mathcal C}\) be the cofibre of tr given in the sequence \(\Sigma B_+\to \Sigma X_+\to {\mathcal C}\). The author shows that there is a spectral sequence \(H^ p_ G(X;\tilde M\otimes h^ q)\Rightarrow h^{p+q}({\mathcal C})\) for any ...
openaire   +2 more sources

Purity, ascent and periodicity for Gorenstein flat cotorsion modules

Journal of the London Mathematical Society, Volume 111, Issue 6, June 2025.
Abstract We investigate purity within the Frobenius category of Gorenstein flat cotorsion modules, which can be seen as an infinitely generated analogue of the Frobenius category of Gorenstein projective objects. As such, the associated stable category can be viewed as an alternative approach to a big singularity category, which is equivalent to Krause'
Isaac Bird
wiley   +1 more source

Quasicategories of Frames of Cofibration Categories [PDF]

Applied Categorical Structures, 2016
The authors show that the quasicategory of frames of a cofibration category, introduced by the second-named author, is equivalent to its simplicial localization. In particular, it follows that given a model category, the quasicategories of frames associated to its underlying cofibration and fibration categories are equivalent. In the very last section,
Kapulkin, Krzysztof, Szumiło, Karol
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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

On the equivalence of Lurie's ∞$\infty$‐operads and dendroidal ∞$\infty$‐operads

Journal of Topology, Volume 17, Issue 4, December 2024.
Abstract In this paper, we prove the equivalence of two symmetric monoidal ∞$\infty$‐categories of ∞$\infty$‐operads, the one defined in Lurie [Higher algebra, available at the author's homepage, http://math.ias.edu/~lurie/, September 2017 version] and the one based on dendroidal spaces.
Vladimir Hinich, Ieke Moerdijk
wiley   +1 more source

Configuration spaces as commutative monoids

Bulletin of the London Mathematical Society, Volume 56, Issue 9, Page 2847-2862, September 2024.
Abstract After one‐point compactification, the collection of all unordered configuration spaces of a manifold admits a commutative multiplication by superposition of configurations. We explain a simple (derived) presentation for this commutative monoid object. Using this presentation, one can quickly deduce Knudsen's formula for the rational cohomology
Oscar Randal‐Williams
wiley   +1 more source

Non‐accessible localizations

Journal of Topology, Volume 17, Issue 2, June 2024.
Abstract In a 2005 paper, Casacuberta, Scevenels, and Smith construct a homotopy idempotent functor E$E$ on the category of simplicial sets with the property that whether it can be expressed as localization with respect to a map f$f$ is independent of the ZFC axioms. We show that this construction can be carried out in homotopy type theory.
J. Daniel Christensen
wiley   +1 more source

On the ∞$\infty$‐topos semantics of homotopy type theory

Bulletin of the London Mathematical Society, Volume 56, Issue 2, Page 461-517, February 2024.
Abstract Many introductions to homotopy type theory and the univalence axiom gloss over the semantics of this new formal system in traditional set‐based foundations. This expository article, written as lecture notes to accompany a three‐part mini course delivered at the Logic and Higher Structures workshop at CIRM‐Luminy, attempt to survey the state of
Emily Riehl
wiley   +1 more source

On the geometric fixed points of real topological cyclic homology

Journal of the London Mathematical Society, Volume 109, Issue 2, February 2024.
Abstract We give a formula for the geometric fixed‐points spectrum of the real topological cyclic homology of a bounded below ring spectrum, as an equaliser of two maps between tensor products of modules over the norm. We then use this formula to carry out computations in the fundamental examples of spherical group rings, perfect Fp$\mathbb {F}_p ...
Emanuele Dotto, Kristian Moi, Irakli Patchkoria   +2 more
wiley   +1 more source