Results 41 to 50 of about 3,998 (234)

Homotopy in statistical physics

Condensed Matter Physics, 2006
In condensed matter physics and related areas, topological defects play important roles in phase transitions and critical phenomena. Homotopy theory facilitates the classification of such topological defects.
R.Kenna
doaj   +1 more source

Revisiting (∞,2)${(\infty,2)}$‐naturality of the Yoneda embedding

Bulletin of the London Mathematical Society, EarlyView.
Abstract We show that the Yoneda embedding ‘is’ (∞,2)$(\infty,2)$‐natural with respect to the functoriality of presheaves via left Kan extension, refining the (∞,1)$(\infty,1)$‐categorical result proven independently by Haugseng–Hebestreit–Linskens–Nuiten and Ramzi, and answering a question of Ben‐Moshe.
Tobias Lenz
wiley   +1 more source

Holography as homotopy

Journal of High Energy Physics
We give an interpretation of holography in the form of the AdS/CFT correspondence in terms of homotopy algebras. A field theory such as a bulk gravity theory can be viewed as a homotopy Lie or L ∞ algebra. We extend this dictionary to theories defined on
Christoph Chiaffrino, Talha Ersoy, Olaf Hohm   +2 more
doaj   +1 more source

Homotopy theory of homotopy algebras [PDF]

Annales de l'Institut Fourier, 2020
This paper studies the homotopy theory of algebras and homotopy algebras over an operad. It provides an exhaustive description of their higher homotopical properties using the more general notion of morphism called infinity-morphism. The method consists in using the operadic calculus to endow the category of coalgebras over the Koszul dual cooperad or ...
openaire   +4 more sources

On computing local monodromy and the numerical local irreducible decomposition

Transactions of the London Mathematical Society, Volume 13, Issue 1, December 2026.
Abstract Similarly to the global case, the local structure of a holomorphic subvariety at a given point is described by its local irreducible decomposition. Geometrically, the key requirement for obtaining a local irreducible decomposition is to compute the local monodromy action of a generic linear projection at the given point, which is always well ...
Parker B. Edwards, Jonathan D. Hauenstein   +1 more
wiley   +1 more source

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

A higher-dimensional categorical perspective on 2-crossed modules

Demonstratio Mathematica
In this study, we will express the 2-crossed module of groups from a higher-dimensional categorical perspective. According to simplicial homotopy theory, a 2-crossed module is the Moore complex of a 2-truncated simplicial group.
Özel Emre, Arslan Ummahan Ege, İlker Akça İbrahim   +2 more
doaj   +1 more source

Spheres over fields, their entire rational maps and applications

Pracì Mìžnarodnogo Geometričnogo Centru
The paper summarizes some results on algebraic geometry presence in the homotopy theory. For the homotopy group πm(Sn), denote by πalgm(Sn) its subset of homotopy classes represented by ℝ-entire rational maps Sm→Sn of spheres.
Marek Golasinski
doaj   +1 more source

Homotopy theory of bicomplexes [PDF]

Journal of Pure and Applied Algebra, 2019
We define two model structures on the category of bicomplexes concentrated in the right half plane. The first model structure has weak equivalences detected by the totalisation functor. The second model structure's weak equivalences are detected by the $E^2$-term of the spectral sequence associated to the filtration of the total complex by the ...
Muro Jiménez, Fernando, Roitzheim, Constanze   +1 more
openaire   +5 more sources