Results 61 to 70 of about 59,724 (184)

Critically fixed Thurston maps: classification, recognition, and twisting

Proceedings of the London Mathematical Society, Volume 132, Issue 3, March 2026.
Abstract An orientation‐preserving branched covering map f:S2→S2$f\colon S^2\rightarrow S^2$ is called a critically fixed Thurston map if f$f$ fixes each of its critical points. It was recently shown that there is an explicit one‐to‐one correspondence between Möbius conjugacy classes of critically fixed rational maps and isomorphism classes of planar ...
Mikhail Hlushchanka, Nikolai Prochorov
wiley   +1 more source

The equivariant topology of stable Kneser graphs [PDF]

Discrete Mathematics & Theoretical Computer Science, 2011
Schrijver introduced the stable Kneser graph $SG_{n,k}, n \geq 1, k \geq 0$. This graph is a vertex critical graph with chromatic number $k+2$, its vertices are certain subsets of a set of cardinality $m=2n+k$.
Carsten Schultz
doaj   +1 more source

The motive of the Hilbert scheme of points in all dimensions

Proceedings of the London Mathematical Society, Volume 132, Issue 3, March 2026.
Abstract We prove a closed formula for the generating series Zd(t)$\mathsf {Z}_d(t)$ of the motives [Hilbd(An)0]$[\operatorname{Hilb}^d({\mathbb {A}}^n)_0]$ in K0(VarC)$K_0(\operatorname{Var}_{{\mathbb {C}}})$ of punctual Hilbert schemes, summing over n$n$, for fixed d>0$d>0$.
Michele Graffeo, Sergej Monavari, Riccardo Moschetti, Andrea T. Ricolfi   +3 more
wiley   +1 more source

Subdivision-based homotopy equivalence of digital circles

Applied General Topology
A direct translation of the notion of homotopy equivalence from algebraic topology to digital images leads to a much more rigid definition in the context of digital topology. This results in two digital circles of different radii being not homotopic.
Samia Ashraf, Madiha Akram, Amna Amanat Ali   +2 more
doaj   +1 more source

Configurations, braids, and homotopy groups [PDF]

Journal of the American Mathematical Society, 2005
Summary: The main results of this article are certain connections between braid groups and the homotopy groups of the \(2\)-sphere. The connections are given in terms of Brunnian braids over the disk and over the \(2\)-sphere. The techniques arise from the natural structure of simplicial and \(\Delta\)-structures on fundamental groups of configuration ...
Berrick, A.J., Cohen, F.R., Wong, Y.L., Wu, J.   +3 more
openaire   +2 more sources

Local equivalence and refinements of Rasmussen's s‐invariant

Journal of Topology, Volume 19, Issue 1, March 2026.
Abstract Inspired by the notions of local equivalence in monopole and Heegaard Floer homology, we introduce a version of local equivalence that combines odd Khovanov homology with equivariant even Khovanov homology into an algebraic package called a local even–odd (LEO) triple.
Nathan M. Dunfield, Robert Lipshitz, Dirk Schütz   +2 more
wiley   +1 more source

The elementary particles as knots in the SU(2) higher homotopy Hopf group

Physics Open
Twelve of the fifteen prime knots with seven or less crossings taken as inclusions in the higher homotopic Hopf group of SU(2) are used to delineate and distinguish the twelve Standard Model quarks and leptons.
Brian Jonathan Wolk
doaj   +1 more source

Milnor invariants of braids and welded braids up to homotopy

, 2020
We consider the group of pure welded braids (also known as loop braids) up to (link-)homotopy. The pure welded braid group classically identifies, via the Artin action, with the group of basis-conjugating automorphisms of the free group, also known as ...
Darné, Jacques
core  

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

Commuting matrices and Atiyah's Real K-theory

, 2019
We describe the $C_2$-equivariant homotopy type of the space of commuting n-tuples in the stable unitary group in terms of Real K-theory. The result is used to give a complete calculation of the homotopy groups of the space of commuting n-tuples in the ...
Gritschacher, Simon, Hausmann, Markus
core   +1 more source