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Related papers: Equivariant Khovanov homotopy types

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We define the orbit category for transitive topological groupoids and their equivariant CW-complexes. By using these constructions we define equivariant Bredon homology and cohomology for actions of transitive topological groupoids. We show…

Algebraic Topology · Mathematics 2019-11-11 Carla Farsi , Laura Scull , Jordan Watts

We define G-pseudovaluations on a variety with a group action G. By introducing G-pseudovaluations, we are able to give some criteria for G-equivariant K-stability of Fano varieties which are parallel to existing results for usual…

Algebraic Geometry · Mathematics 2020-07-31 Ziwen Zhu

Connections between homotopy theory and type theory have recently attracted a lot of attention, with Voevodsky's univalent foundations and the interpretation of Martin-Lof's identity types in Quillen model categories as some of the…

Category Theory · Mathematics 2016-09-21 Benno van den Berg

We prove that the homotopy theory of cofibration categories is equivalent to the homotopy theory of cocomplete quasicategories. This is achieved by presenting both homotopy theories as fibration categories and constructing an explicit…

Algebraic Topology · Mathematics 2014-11-04 Karol Szumiło

We prove a number of results of the following common flavor: for a category $\mathcal{C}$ of topological or uniform spaces with all manner of other properties of common interest (separation / completeness / compactness axioms), a group (or…

Category Theory · Mathematics 2025-11-10 Alexandru Chirvasitu

We introduce and study equivariant Seiberg-Witten invariants for $4$-manifolds equipped with a smooth action of a finite group $G$. Our invariants come in two types: cohomological, valued in the group cohomology of $G$ and $K$-theoretic,…

Differential Geometry · Mathematics 2024-06-04 David Baraglia

A periodic link, is link in $S^3$ with action of $\mathbb{Z}_p$ by rotation with $2\pi/p$ around a fixed unknot $U$. The equivariant Khovanov homology of periodic links has been studied in \cite{BP17}. We prove that the equivariant Khovanov…

Geometric Topology · Mathematics 2025-09-03 Siavash Jafarizadeh

In a previous paper, we defined a space-level version X(L) of Khovanov homology. This induces an action of the Steenrod algebra on Khovanov homology. In this paper, we describe the first interesting operation, Sq^2:Kh^{i,j}(L) ->…

Geometric Topology · Mathematics 2021-11-09 Robert Lipshitz , Sucharit Sarkar

Given a topological group G, its orbit category Orb_G has the transitive G-spaces G/H as objects and the G-equivariant maps between them as morphisms. A well known theorem of Elmendorf then states that the category of G-spaces and the…

Algebraic Topology · Mathematics 2007-05-23 Andre Henriques , David Gepner

A global action is the algebraic analogue of a topological manifold. This construction was introduced in first place by A. Bak as a combinatorial approach to K-Theory and the concept was later generalized by Bak, Brown, Minian and Porter to…

Algebraic Topology · Mathematics 2018-07-10 Matias Luis del Hoyo , Elias Gabriel Minian

The purpose of this paper is to interpret polynomial invariants of strongly invertible links in terms of Khovanov homology theory. To a divide, that is a proper generic immersion of a finite number of copies of the unit interval and circles…

Algebraic Topology · Mathematics 2010-02-26 Olivier Couture

We consider bifurcation of critical points from a trivial branch for families of functionals that are invariant under the orthogonal action of a compact Lie group. Based on a recent construction of an equivariant spectral flow by the…

Functional Analysis · Mathematics 2023-06-05 Marek Izydorek , Joanna Janczewska , Maciej Starostka , Nils Waterstraat

We prove that the bigraded colored Khovanov-Rozansky type A link and tangle invariants are functorial with respect to link and tangle cobordisms.

Geometric Topology · Mathematics 2019-03-20 Michael Ehrig , Daniel Tubbenhauer , Paul Wedrich

Khovanov homology is an invariant for links in the three sphere that categorizes the Jones polynomial. We extend Khovanov's construction to links in 3-manifolds that are connected sums of orientable interval bundles over surfaces. Cutting…

Geometric Topology · Mathematics 2026-03-10 Alan Du

In the mid 1980s, while working on establishing completion theorems for equivariant Algebraic K-Theory similar to the well-known completion theorems for equivariant topological K-theory, the late Robert Thomason found the strong finiteness…

Algebraic Geometry · Mathematics 2024-05-17 Gunnar Carlsson , Roy Joshua , Pablo Pelaez

We define a Khovanov-Lipshitz-Sarkar stable homotopy type for the homotopical Khovanov homology of links in the thickened torus after the authors introduced that in the case of higher genus surfaces in the previous paper of this one.

Geometric Topology · Mathematics 2025-09-18 Louis H. Kauffman , Igor Mikhailovich Nikonov , Eiji Ogasa

Starting from any proper action of any locally compact quantum group on any discrete quantum space, we show that its equivariant representation theory yields a concrete unitary 2-category of finite type Hilbert bimodules over the discrete…

Operator Algebras · Mathematics 2025-08-27 Lukas Rollier

We introduce an invariant of tangles in Khovanov homology by considering a natural inverse system of Khovanov homology groups. As application, we derive an invariant of strongly invertible knots; this invariant takes the form of a graded…

Geometric Topology · Mathematics 2017-04-07 Liam Watson

We describe various path homology theories constructed for a directed hypergraph. We introduce the category of directed hypergraphs and the notion of a homotopy in this category. Also, we investigate the functoriality and the homotopy…

Algebraic Topology · Mathematics 2021-09-22 Yuri Muranov , Anna Szczepkowska , Vladimir Vershinin

We construct an equivariant version of annular Khovanov homology via the Frobenius algebra associated with $U(1) \times U(1)$-equivariant cohomology of $\mathbb{CP}^1$. Motivated by the relationship between the Temperley-Lieb algebra and…

Quantum Algebra · Mathematics 2020-08-04 Rostislav Akhmechet