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On modular cohomotopy groups.
- Source :
- Israel Journal of Mathematics; Mar2023, Vol. 253 Issue 2, p887-915, 29p
- Publication Year :
- 2023
-
Abstract
- Let p be a prime and let π<superscript>n</superscript>(X; ℤ/p<superscript>r</superscript>) = [X, M<subscript>n</subscript>(ℤ/p<superscript>r</superscript>)] be the set of homotopy classes of based maps from CW-complexes X into the mod p<superscript>r</superscript> Moore spaces M<subscript>n</subscript>(ℤ/p<superscript>r</superscript>) of degree n, where ℤ/p<superscript>r</superscript> denotes the integers mod p<superscript>r</superscript>. In this paper we firstly determine the modular cohomotopy groups π<superscript>n</superscript>(X; ℤ/p<superscript>r</superscript>) up to extensions by classical methods of primary cohomology operations and give conditions for the splitness of the extensions. Secondly we utilize some unstable homotopy theory of Moore spaces to study the modular cohomotopy groups; especially, the group π<superscript>3</superscript>(X; ℤ<subscript>(2)</subscript>) with dim(X) ≤ 6 is determined. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00212172
- Volume :
- 253
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Israel Journal of Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 163486886
- Full Text :
- https://doi.org/10.1007/s11856-022-2409-0