Geodesic
On products of beta and gamma elements in the homotopy of the first Smith–Toda spectrum
Shimomura, Katsumi1 ; Shimomura, Mao-no-suke2
1 Department of Mathematics, Faculty of Science, Kochi University, Kochi, Japan
2 Department of Mathematics, Faculty of Science and Technology, Kochi University, Kochi, Japan
Algebraic and Geometric Topology, Tome 24 (2024) no. 7, pp. 3875-3896

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We determine the first cohomology of the monochromatic comodule M21 at an odd prime, and apply the results to show nontrivialities of some products of beta and gamma elements in the homotopy groups of the Smith–Toda spectrum V (1). The cohomology for a prime greater than three was previously determined by the first author. Here we verify them and determine the cohomology at the prime 3 by elementary calculation. The cohomology will be a stepping stone for computing the cohomology of the monochromatic comodule M03, which we hope to determine for a long time.

DOI : 10.2140/agt.2024.24.3875
Keywords: Smith–Toda spectra, stable homotopy groups, Greek letter elements, monochromatic comodules

Shimomura, Katsumi 1 ; Shimomura, Mao-no-suke 2

1 Department of Mathematics, Faculty of Science, Kochi University, Kochi, Japan
2 Department of Mathematics, Faculty of Science and Technology, Kochi University, Kochi, Japan 
@article{10_2140_agt_2024_24_3875,
     author = {Shimomura, Katsumi and Shimomura, Mao-no-suke},
     title = {On products of beta and gamma elements in the homotopy of the first {Smith{\textendash}Toda} spectrum},
     journal = {Algebraic and Geometric Topology},
     pages = {3875--3896},
     publisher = {mathdoc},
     volume = {24},
     number = {7},
     year = {2024},
     doi = {10.2140/agt.2024.24.3875},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.3875/}
}
TY  - JOUR
AU  - Shimomura, Katsumi
AU  - Shimomura, Mao-no-suke
TI  - On products of beta and gamma elements in the homotopy of the first Smith–Toda spectrum
JO  - Algebraic and Geometric Topology
PY  - 2024
SP  - 3875
EP  - 3896
VL  - 24
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.3875/
DO  - 10.2140/agt.2024.24.3875
ID  - 10_2140_agt_2024_24_3875
ER  - 
%0 Journal Article
%A Shimomura, Katsumi
%A Shimomura, Mao-no-suke
%T On products of beta and gamma elements in the homotopy of the first Smith–Toda spectrum
%J Algebraic and Geometric Topology
%D 2024
%P 3875-3896
%V 24
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.3875/
%R 10.2140/agt.2024.24.3875
%F 10_2140_agt_2024_24_3875
Shimomura, Katsumi; Shimomura, Mao-no-suke. On products of beta and gamma elements in the homotopy of the first Smith–Toda spectrum. Algebraic and Geometric Topology, Tome 24 (2024) no. 7, pp. 3875-3896. doi: 10.2140/agt.2024.24.3875

Cité par Sources :