Comultiplications on the Localized Spheres and Moore Spaces

Dae-Woong Lee
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Dae-Woong Lee: Department of Mathematics, and Institute of Pure and Applied Mathematics, Jeonbuk National University, 567 Baekje-daero, Deokjin-gu, Jeonju-si, Jeollabuk-do 54896, Korea

Mathematics, 2020, vol. 8, issue 1, 1-19

Abstract: Any nilpotent CW-space can be localized at primes in a similar way to the localization of a ring at a prime number. For a collection P of prime numbers which may be empty and a localization X P of a nilpotent CW-space X at P , we let | C ( X ) | and | C ( X P ) | be the cardinalities of the sets of all homotopy comultiplications on X and X P , respectively. In this paper, we show that if | C ( X ) | is finite, then | C ( X ) | ≥ | C ( X P ) | , and if | C ( X ) | is infinite, then | C ( X ) | = | C ( X P ) | , where X is the k -fold wedge sum ? i = 1 k S n i or Moore spaces M ( G , n ) . Moreover, we provide examples to concretely determine the cardinality of homotopy comultiplications on the k -fold wedge sum of spheres, Moore spaces, and their localizations.

Keywords: comultiplications; localized spheres; basic Whitehead products; Hilton formula; Moore space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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