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Retractions of {$H$}-spaces
- Source :
- Hiroshima Math. J. 35, no. 1 (2005), 159-165
- Publication Year :
- 2005
- Publisher :
- Hiroshima University, Department of Mathematics, 2005.
-
Abstract
- Stasheff showed that if a map between H-spaces is an H-map, then the suspension of the map is extendable to a map between cprojective planes of the H-spaces. Stahseff also proved the converse under the assumption that the multiplication of the target space of the map is homotopy associative. We show by giving an example that the assumption of homotopy associativity of the multiplication of the target space is necessary to show the converse. We also show an analogous fact for maps between higher homotopy associative H-spaces.<br />6 pages
- Subjects :
- Discrete mathematics
Pure mathematics
Algebra and Number Theory
Homotopy lifting property
Homotopy
Suspension (topology)
Mathematics::Algebraic Topology
Regular homotopy
n-connected
Homotopy sphere
Mathematics::Category Theory
Loop space
FOS: Mathematics
Algebraic Topology (math.AT)
Multiplication
Geometry and Topology
Mathematics - Algebraic Topology
55P45
Analysis
Mathematics
55P45 (Primary) 55R35 (Secondary)
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Hiroshima Math. J. 35, no. 1 (2005), 159-165
- Accession number :
- edsair.doi.dedup.....1ebe3b806e9c172beb78459e12f7ea17