# Homotopy - Explore the Science & Experts | ideXlab

## Homotopy

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### Matthew Stoffregen – One of the best experts on this subject based on the ideXlab platform.

• ##### an odd khovanov Homotopy type
Co-Authors: Sucharit Sarkar, Christopher Scaduto, Matthew Stoffregen
Abstract:

Abstract For each link L ⊂ S 3 and every quantum grading j, we construct a stable Homotopy type X o j ( L ) whose cohomology recovers Ozsvath-Rasmussen-Szabo’s odd Khovanov homology, H ˜ i ( X o j ( L ) ) = Kh o i , j ( L ) , following a construction of Lawson-Lipshitz-Sarkar of the even Khovanov stable Homotopy type. Furthermore, the odd Khovanov Homotopy type carries a Z / 2 action whose fixed point set is a desuspension of the even Khovanov Homotopy type. We also construct a potentially new even Khovanov Homotopy type with a Z / 2 action, with fixed point set a desuspension of X o j ( L ) .

• ##### an odd khovanov Homotopy type
arXiv: Geometric Topology, 2018
Co-Authors: Sucharit Sarkar, Christopher Scaduto, Matthew Stoffregen
Abstract:

For each link L in S^3 and every quantum grading j, we construct a stable Homotopy type X^j_o(L) whose cohomology recovers Ozsvath-Rasmussen-Szabo’s odd Khovanov homology, H_i(X^j_o(L)) = Kh^{i,j}_o(L), following a construction of Lawson-Lipshitz-Sarkar of the even Khovanov stable Homotopy type. Furthermore, the odd Khovanov Homotopy type carries a Z/2 action whose fixed point set is a desuspension of the even Khovanov Homotopy type. We also construct a Z/2 action on an even Khovanov Homotopy type, with fixed point set a desuspension of X^j_o(L).

### Sucharit Sarkar – One of the best experts on this subject based on the ideXlab platform.

• ##### an odd khovanov Homotopy type
Co-Authors: Sucharit Sarkar, Christopher Scaduto, Matthew Stoffregen
Abstract:

Abstract For each link L ⊂ S 3 and every quantum grading j, we construct a stable Homotopy type X o j ( L ) whose cohomology recovers Ozsvath-Rasmussen-Szabo’s odd Khovanov homology, H ˜ i ( X o j ( L ) ) = Kh o i , j ( L ) , following a construction of Lawson-Lipshitz-Sarkar of the even Khovanov stable Homotopy type. Furthermore, the odd Khovanov Homotopy type carries a Z / 2 action whose fixed point set is a desuspension of the even Khovanov Homotopy type. We also construct a potentially new even Khovanov Homotopy type with a Z / 2 action, with fixed point set a desuspension of X o j ( L ) .

• ##### an odd khovanov Homotopy type
arXiv: Geometric Topology, 2018
Co-Authors: Sucharit Sarkar, Christopher Scaduto, Matthew Stoffregen
Abstract:

For each link L in S^3 and every quantum grading j, we construct a stable Homotopy type X^j_o(L) whose cohomology recovers Ozsvath-Rasmussen-Szabo’s odd Khovanov homology, H_i(X^j_o(L)) = Kh^{i,j}_o(L), following a construction of Lawson-Lipshitz-Sarkar of the even Khovanov stable Homotopy type. Furthermore, the odd Khovanov Homotopy type carries a Z/2 action whose fixed point set is a desuspension of the even Khovanov Homotopy type. We also construct a Z/2 action on an even Khovanov Homotopy type, with fixed point set a desuspension of X^j_o(L).

### Hansjoachim Baues – One of the best experts on this subject based on the ideXlab platform.

• ##### Secondary Homotopy groups
Forum Mathematicum, 2006
Co-Authors: Hansjoachim Baues, Fernando Muro
Abstract:

Secondary Homotopy groups supplement the structure of classical Homotopy groups. They yield a track functor on the track category of pointed spaces compatible with fiber sequences, suspensions and loop spaces. They also yield algebraic models of Homotopy types with Homotopy groups concentrated in two consecutive dimensions.

• ##### Homotopy type and homology
, 1996
Co-Authors: Hansjoachim Baues
Abstract:

Introduction 1. Linear extension and Moore spaces 2. Invariants of Homotopy types 3. On the classification of Homotopy types 4. The CW-tower of categories 5. Spaniert-Whitehead duality and the stable CW-tower 6. Eilenberg-Mac Lane functors 7. Moore functors 8. The Homotopy category of (n -1)-connected (n+1)-types 8. On the Homotopy classification of (n-1)-connected (n+3)-dimensional polyhedra, n>4 9. On the Homotopy classification of 2-connected 6-dimensional polyhedra 10. Decomposition of Homotopy types 11. Homotopy groups in dimension 4 12. On the Homotopy classification of simply connected 5-dimensional polyhedra 13. Primary Homotopy operations and Homotopy groups of mapping cones Bibliography Index

• ##### Handbook of Algebraic Topology – CHAPTER 1 – Homotopy Types
Handbook of Algebraic Topology, 1995
Co-Authors: Hansjoachim Baues
Abstract:

This chapter provides an overview of Homotopy types. The theory of Homotopy types is one of the most basic parts of topology and geometry. At the center of this theory stands the concept of algebraic invariants. Homotopy types are equivalence classes, Homotopy types, and homeomorphism types.. To this end, one uses the notion of deformation or Homotopy. The principal idea is to consider “nearby” objects (that is, objects, which are “deformed” or “perturbed” continuously a little bit) as being similar. This idea of perturbation is a common one in mathematics and science. The properties that remain valid under small perturbations are considered the stable and essential features of an object. Homotopy types of polyhedra are archetypes underlying most geometric structures. There are many different topological and combinatorial devices that can be used to construct the Homotopy types of connected polyhedra, for example, simplicial complexes, simplicial sets, CW-complexes, topological spaces, simplicial groups, small categories, and partially ordered sets.

### J. Rosicky – One of the best experts on this subject based on the ideXlab platform.

• ##### On Homotopy varieties
Co-Authors: J. Rosicky
Abstract:

Given an algebraic theory T, a Homotopy T-algebra is a simplicial set where all equations from T hold up to Homotopy. All Homotopy T-algebras form a Homotopy variety. We will give a characterization of Homotopy varieties analogous to the characterization of varieties.

• ##### On Homotopy varieties
arXiv: Category Theory, 2005
Co-Authors: J. Rosicky
Abstract:

Given an algebraic theory \$\ct\$, a Homotopy \$\ct\$-algebra is a simplicial set where all equations from \$\ct\$ hold up to Homotopy. All Homotopy \$\ct\$-algebras form a Homotopy variety. We give a characterization of Homotopy varieties analogous to the characterization of varieties. We will also study Homotopy models of limit theories which leads to Homotopy locally presentable categories. These were recently considered by Simpson, Lurie, To\”{e}n and Vezzosi.

### A Rajabi – One of the best experts on this subject based on the ideXlab platform.

• ##### assessment of Homotopy perturbation and perturbation methods in heat radiation equations
International Communications in Heat and Mass Transfer, 2006
Co-Authors: D D Ganji, A Rajabi
Abstract:

One of the newest analytical methods to solve the nonlinear heat transfer equations is using both Homotopy and perturbation methods in equations. Here, Homotopy–perturbation method is applied to solve heat transfer problems with high nonlinearity order. The origin of using this method is the difficulties and limitations of perturbation or Homotopy. It has been attempted to show the capabilities and wide-range applications of the Homotopy–perturbation method in comparison with the previous ones in solving heat transfer problems. In this research, Homotopy–perturbation method is used to solve an unsteady nonlinear convective-radiative equation and a nonlinear convective-radiative conduction equation containing two small parameters of e1 and e2.