Geodesic
On the existence of a $v^{32}_2$-self map on $M(1,4)$ at the prime 2
Homology, homotopy, and applications, Tome 10 (2008) no. 3, pp. 45-84.

Voir la notice de l'article provenant de la source International Press of Boston

Let $M(1)$ be the mod $2$ Moore spectrum. J.F. Adams proved that $M(1)$ admits a minimal $v_1$-self map $v_1^4 \colon \Sigma^8 M(1) \rightarrow M(1)$. Let $M(1,4)$ be the cofiber of this self-map. The purpose of this paper is to prove that $M(1,4)$ admits a minimal $v_2$-self map of the form $v_2^{32} \colon \Sigma^{192} M(1,4) \rightarrow M(1,4)$. The existence of this map implies the existence of many $192$-periodic families of elements in the stable homotopy groups of spheres.
DOI : 10.4310/HHA.2008.v10.n3.a4
Classification : 55Q51, 55Q40
Keywords: $v2$-periodicity, stable homotopy 
@article{HHA_2008_10_3_a6,
     author = {M. Behrens and M. Hill and M.J. Hopkins and M. Mahowald},
     title = {On the existence of a $v^{32}_2$-self map on $M(1,4)$ at the prime 2},
     journal = {Homology, homotopy, and applications},
     pages = {45--84},
     publisher = {mathdoc},
     volume = {10},
     number = {3},
     year = {2008},
     doi = {10.4310/HHA.2008.v10.n3.a4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2008.v10.n3.a4/}
}
TY  - JOUR
AU  - M. Behrens
AU  - M. Hill
AU  - M.J. Hopkins
AU  - M. Mahowald
TI  - On the existence of a $v^{32}_2$-self map on $M(1,4)$ at the prime 2
JO  - Homology, homotopy, and applications
PY  - 2008
SP  - 45
EP  - 84
VL  - 10
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4310/HHA.2008.v10.n3.a4/
DO  - 10.4310/HHA.2008.v10.n3.a4
LA  - en
ID  - HHA_2008_10_3_a6
ER  - 
%0 Journal Article
%A M. Behrens
%A M. Hill
%A M.J. Hopkins
%A M. Mahowald
%T On the existence of a $v^{32}_2$-self map on $M(1,4)$ at the prime 2
%J Homology, homotopy, and applications
%D 2008
%P 45-84
%V 10
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4310/HHA.2008.v10.n3.a4/
%R 10.4310/HHA.2008.v10.n3.a4
%G en
%F HHA_2008_10_3_a6
M. Behrens; M. Hill; M.J. Hopkins; M. Mahowald. On the existence of a $v^{32}_2$-self map on $M(1,4)$ at the prime 2. Homology, homotopy, and applications, Tome 10 (2008) no. 3, pp. 45-84. doi : 10.4310/HHA.2008.v10.n3.a4. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2008.v10.n3.a4/

Cité par Sources :