Results 21 to 30 of about 74 (59)

The six operations in topology

Journal of Topology, Volume 18, Issue 4, December 2025.
Abstract In this paper, we show that the six functor formalism for sheaves on locally compact Hausdorff topological spaces, as developed, for example,‐ in Kashiwara and Schapira's book Sheaves on Manifolds, can be extended to sheaves with values in any closed symmetric monoidal ∞$\infty$‐category which is stable and bicomplete. Notice that, since we do
Marco Volpe
wiley   +1 more source

A topological algorithm for the Fourier transform of Stokes data at infinity

Journal of the London Mathematical Society, Volume 112, Issue 2, August 2025.
Abstract We give a topological description of the behaviour of Stokes matrices under the Fourier transform from infinity to infinity in a large number of cases of one level. This explicit, algorithmic statement is obtained by building on a recent result of T.
Jean Douçot, Andreas Hohl
wiley   +1 more source

The Hilton–Milnor theorem in higher topoi

Bulletin of the London Mathematical Society, Volume 57, Issue 5, Page 1468-1481, May 2025.
Abstract In this note, we show that the classical theorem of Hilton–Milnor on finite wedges of suspension spaces remains valid in an arbitrary ∞$\infty$‐topos. Our result relies on a version of James' splitting proved in [Devalapurkar and Haine, Doc. Math.
Samuel Lavenir
wiley   +1 more source

Non‐isotopic splitting spheres for a split link in S4$S^4$

Proceedings of the London Mathematical Society, Volume 130, Issue 4, April 2025.
Abstract We show that there exist split, orientable, 2‐component surface‐links in S4$S^4$ with non‐isotopic splitting spheres in their complements. In particular, for non‐negative integers m,n$m,n$ with m⩾4$m\geqslant 4$, the unlink Lm,n$L_{m,n}$ consisting of one component of genus m$m$ and one component of genus n$n$ contains in its complement two ...
Mark Hughes, Seungwon Kim, Maggie Miller
wiley   +1 more source

On the parameterized Tate construction

Journal of Topology, Volume 18, Issue 1, March 2025.
Abstract We introduce and study a genuine equivariant refinement of the Tate construction associated to an extension Ĝ$\widehat{G}$ of a finite group G$G$ by a compact Lie group K$K$, which we call the parameterized Tate construction (−)tGK$(-)^{t_G K}$.
J. D. Quigley, Jay Shah
wiley   +1 more source

Cluster categories for completed infinity‐gons I: Categorifying triangulations

Journal of the London Mathematical Society, Volume 111, Issue 2, February 2025.
Abstract Paquette and Yıldırım recently introduced triangulated categories of arcs in completed infinity‐gons, which are discs with an infinite closed set of marked points on their boundary. These categories have many features in common with the cluster categories associated to discs with different sets of marked points. In particular, they have (weak)
İlke Çanakçı, Martin Kalck, Matthew Pressland   +2 more
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

Metrics of positive Ricci curvature on simply‐connected manifolds of dimension 6k$6k$

Journal of Topology, Volume 17, Issue 4, December 2024.
Abstract A consequence of the surgery theorem of Gromov and Lawson is that every closed, simply‐connected 6‐manifold admits a Riemannian metric of positive scalar curvature. For metrics of positive Ricci curvature, it is widely open whether a similar result holds; there are no obstructions known for those manifolds to admit a metric of positive Ricci ...
Philipp Reiser
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

A 2-groupoid Characterisation of the Cubical Homotopy Pushout

Applied Categorical Structures, 2004
The mapping cone, a concept that plays an important role in algebraic topology, took on a categorical flavour as a homotopy colimit and its relation to the fundamental groupoid of a function space was recorded in [\textit{M. Mather}, Can. J. Math. 28, 225-263 (1976; Zbl 0351.55005)]. General treatments of homotopy limits and homotopy colimits are known,
Hardie, K. A., Kamps, K. H., Witbooi, P. J.   +2 more
openaire   +3 more sources