Comultiplications on a wedge of two spheres
type: Item
instance of: scholarly article
title: Comultiplications on a wedge of two spheres
zbMATH Open document ID: 1229.55009
author: Martin Arkowitz
author: Dae-Woong Lee
published in: Science China. Mathematics
publication date: 2011-07-01T00:00:00Z
review text: The first author of this paper showed in [Co-H-spaces. James, I. M. (ed.), Handbook of algebraic topology. Amsterdam: North-Holland. 1143--1173 (1995; Zbl 0941.55001)] that the comultiplication of the \(n\)-sphere with \(n\geq2\) is unique and commutative up to homotopy. On the other hand, for a wedge of two spheres, it is known that there are many comultiplications with many different properties. In this paper, the authors show that the number of comultiplications on a wedge of two spheres is the product of the order of the homotopy groups of certain spheres. The authors also study the conditions for each comultiplication to be homotopy associative or homotopy commutative.
reviewed by: Yutaka Hemmi
Mathematics Subject Classification ID: 55Q25
Mathematics Subject Classification ID: 55Q15
Mathematics Subject Classification ID: 55P40
zbMATH DE Number: 5916766
zbMATH Keywords: co-H-spaces
zbMATH Keywords: comultiplications
zbMATH Keywords: homotopy associativity
zbMATH Keywords: homotopy commutativity
zbMATH Keywords: basic Whitehead products
zbMATH Keywords: Hilton's formula
zbMATH Keywords: Hopf-Hilton invariants
MaRDI profile type: Publication
full work available at URL: s11425-010-4061-0
OpenAlex ID: W2015070995
cites work: Q4896559
cites work: Comultiplications on free groups and wedges of circles
cites work: Rational co-H-spaces
cites work: Equivalence classes of homotopy-associative comultiplications of finite complexes
cites work: Q5730670
cites work: Category and generalized Hopf invariants
cites work: Cogroups and suspensions
cites work: On the Homotopy Groups of the Union of Spheres
cites work: On the number of comultiplications of a suspension
cites work: Compositional Methods in Homotopy Groups of Spheres. (AM-49)
DOI: 10.1007/S11425-010-4061-0
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description: scientific article; zbMATH DE number 5916766