Infinite families of higher torsion in the homotopy groups of Moore spaces

被引：0

作者：

Amelotte, Steven ^{[1
]}

Cohen, Frederick R. ^{[2
]}

Luo, Yuxin ^{[2
]}

机构：

[1] Western Univ, Dept Math, London, ON, Canada

[2] Univ Rochester, Dept Math, Rochester, NY USA

来源：

ALGEBRAIC AND GEOMETRIC TOPOLOGY | 2023年 / 23卷 / 05期

基金：

美国国家科学基金会;

关键词：

DOUBLE LOOPS; DECOMPOSITION; PERIODICITY; EXPONENTS;

D O I：

10.2140/agt.2023.23.2389

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a refinement of the stable Snaith splitting of the double loop space of a Moore space and use it to construct infinite periodic families of elements of order pr +1 in the homotopy groups of mod pr Moore spaces. For odd primes p, our splitting implies that the homotopy groups of the mod pr +1 Moore spectrum are summands of the unstable homotopy groups of each mod pr Moore space.

引用

页码：2389 / 2414

页数：27

共 50 条

[21] ON HOMOTOPY GROUPS OF HOMOGENEOUS SPACES
HU, ST
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1952, 58 (01) : 70 - 70
[22] HOMOTOPY GROUPS OF SPACES OF EMBEDDINGS
LUSK, EL
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1970, 17 (03): : 527 - &
[23] INFINITE SYSTOLIC GROUPS ARE NOT TORSION
Prytula, Tomasz
COLLOQUIUM MATHEMATICUM, 2018, 153 (02) : 169 - 194
[24] EVERY COMMUTATIVE SQUARE OF ABELIAN-GROUPS CAN BE REALIZED BY A HOMOTOPY COMMUTATIVE SQUARE OF MOORE, OR CO-MOORE, SPACES
KAINEN, PC
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1972, 5 (NOV): : 577 - &
[25] Homotopy categories for simply connected torsion spaces
Paricio, LJH
APPLIED CATEGORICAL STRUCTURES, 2005, 13 (5-6) : 421 - 451
[26] TORSION IN HOMOTOPY ASSOCIATIVE H-SPACES
KANE, R
ILLINOIS JOURNAL OF MATHEMATICS, 1976, 20 (03) : 476 - 485
[27] Homotopy Categories for Simply Connected Torsion Spaces
Luis Javier Hernández Paricio
Applied Categorical Structures, 2005, 13 : 421 - 451
[28] NEW INFINITE FAMILIES IN STABLE HOMOTOPY OF SPHERES
SMITH, L
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 81 (01) : 148 - 150
[29] On the homotopy category of moore spaces and an old result of barrat
1600, Publ by Springer-Verlag Berlin, Berlin 33, Ger (1474):
[30] ON THE HOMOTOPY CATEGORY OF MOORE SPACES AND AN OLD RESULT OF BARRATT
BAUES, HJ
LECTURE NOTES IN MATHEMATICS, 1991, 1474 : 207 - 230

← 1 2 3 4 5 →