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On modular cohomotopy groups.

Authors :
Li, Pengcheng
Pan, Jianzhong
Wu, Jie
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