Homotopy comultiplications on the k-fold wedge of spheres

Dae Woong Lee; Sunyoung Lee

doi:10.1016/j.topol.2019.01.001

Homotopy comultiplications on the k-fold wedge of spheres

Dae Woong Lee^*
, Sunyoung Lee

^*Corresponding author for this work

Department of Mathematics

Jeonbuk National University

Research output: Contribution to journal › Journal article › peer-review

15 Scopus citations

Abstract

Regarding the calculation of homotopy classes of comultiplications on a wedge of spheres, the more spheres that appear in the wedge, the more complicated proofs and computations become. In this paper, we concentrate on the calculations of the comultiplications and the associative and commutative comultiplications on the k-fold wedge of spheres ∨_i=1 ^kS^n_i for sufficiently large values of k as a generalization of the papers [3,4]. In particular, we observe extraordinary regularities and patterns on the conditions of associative and commutative comultiplications on the k-fold wedge of spheres.

Original language	English
Pages (from-to)	145-170
Number of pages	26
Journal	Topology and its Applications
Volume	254
DOIs	https://doi.org/10.1016/j.topol.2019.01.001
State	Published - 2019.03.1

Keywords

Basic Whitehead product
Co-H-space
Comultiplication
Height
Hilton's theorem
Homotopy associativity
Homotopy commutativity
Hopf–Hilton invariant
Perturbation

Quacquarelli Symonds(QS) Subject Topics

Mathematics

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10.1016/j.topol.2019.01.001

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title = "Homotopy comultiplications on the k-fold wedge of spheres",

abstract = "Regarding the calculation of homotopy classes of comultiplications on a wedge of spheres, the more spheres that appear in the wedge, the more complicated proofs and computations become. In this paper, we concentrate on the calculations of the comultiplications and the associative and commutative comultiplications on the k-fold wedge of spheres ∨i=1 kSni for sufficiently large values of k as a generalization of the papers [3,4]. In particular, we observe extraordinary regularities and patterns on the conditions of associative and commutative comultiplications on the k-fold wedge of spheres.",

keywords = "Basic Whitehead product, Co-H-space, Comultiplication, Height, Hilton's theorem, Homotopy associativity, Homotopy commutativity, Hopf–Hilton invariant, Perturbation",

author = "Lee, \{Dae Woong\} and Sunyoung Lee",

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier B.V.",

year = "2019",

month = mar,

day = "1",

doi = "10.1016/j.topol.2019.01.001",

language = "English",

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journal = "Topology and its Applications",

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TY - JOUR

T1 - Homotopy comultiplications on the k-fold wedge of spheres

AU - Lee, Dae Woong

AU - Lee, Sunyoung

PY - 2019/3/1

Y1 - 2019/3/1

N2 - Regarding the calculation of homotopy classes of comultiplications on a wedge of spheres, the more spheres that appear in the wedge, the more complicated proofs and computations become. In this paper, we concentrate on the calculations of the comultiplications and the associative and commutative comultiplications on the k-fold wedge of spheres ∨i=1 kSni for sufficiently large values of k as a generalization of the papers [3,4]. In particular, we observe extraordinary regularities and patterns on the conditions of associative and commutative comultiplications on the k-fold wedge of spheres.

AB - Regarding the calculation of homotopy classes of comultiplications on a wedge of spheres, the more spheres that appear in the wedge, the more complicated proofs and computations become. In this paper, we concentrate on the calculations of the comultiplications and the associative and commutative comultiplications on the k-fold wedge of spheres ∨i=1 kSni for sufficiently large values of k as a generalization of the papers [3,4]. In particular, we observe extraordinary regularities and patterns on the conditions of associative and commutative comultiplications on the k-fold wedge of spheres.

KW - Basic Whitehead product

KW - Co-H-space

KW - Comultiplication

KW - Height

KW - Hilton's theorem

KW - Homotopy associativity

KW - Homotopy commutativity

KW - Hopf–Hilton invariant

KW - Perturbation

UR - https://www.scopus.com/pages/publications/85059626690

U2 - 10.1016/j.topol.2019.01.001

DO - 10.1016/j.topol.2019.01.001

M3 - Journal article

AN - SCOPUS:85059626690

SN - 0166-8641

VL - 254

SP - 145

EP - 170

JO - Topology and its Applications

JF - Topology and its Applications

ER -

Homotopy comultiplications on the k-fold wedge of spheres

Abstract

Keywords

Quacquarelli Symonds(QS) Subject Topics

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