# Co-H-structures on equivariant Moore spaces

Martin Arkowitz; Marek Golasiński

Fundamenta Mathematicae (1994)

- Volume: 146, Issue: 1, page 59-67
- ISSN: 0016-2736

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topArkowitz, Martin, and Golasiński, Marek. "Co-H-structures on equivariant Moore spaces." Fundamenta Mathematicae 146.1 (1994): 59-67. <http://eudml.org/doc/212051>.

@article{Arkowitz1994,

abstract = {Let G be a finite group, $\mathbb \{O\}_G$ the category of canonical orbits of G and $A : \mathbb \{O\}_G → \mathbb \{A\}$b a contravariant functor to the category of abelian groups. We investigate the set of G-homotopy classes of comultiplications of a Moore G-space of type (A,n) where n ≥ 2 and prove that if such a Moore G-space X is a cogroup, then it has a unique comultiplication if dim X < 2n - 1. If dim X = 2n-1, then the set of comultiplications of X is in one-one correspondence with $Ext^\{n-1\}(A, A ⊗ A)$. Then the case $G = ℤ_\{p^k\}$ leads to an example of infinitely many G-homotopically distinct G-maps $φ_i : X → Y$ such that $φ_i^H$, $φ_j^H : X^H → Y^H$ are homotopic for all i,j and all subgroups H ⊆ G.},

author = {Arkowitz, Martin, Golasiński, Marek},

journal = {Fundamenta Mathematicae},

keywords = {homotopy classes of comultiplications; Moore -space},

language = {eng},

number = {1},

pages = {59-67},

title = {Co-H-structures on equivariant Moore spaces},

url = {http://eudml.org/doc/212051},

volume = {146},

year = {1994},

}

TY - JOUR

AU - Arkowitz, Martin

AU - Golasiński, Marek

TI - Co-H-structures on equivariant Moore spaces

JO - Fundamenta Mathematicae

PY - 1994

VL - 146

IS - 1

SP - 59

EP - 67

AB - Let G be a finite group, $\mathbb {O}_G$ the category of canonical orbits of G and $A : \mathbb {O}_G → \mathbb {A}$b a contravariant functor to the category of abelian groups. We investigate the set of G-homotopy classes of comultiplications of a Moore G-space of type (A,n) where n ≥ 2 and prove that if such a Moore G-space X is a cogroup, then it has a unique comultiplication if dim X < 2n - 1. If dim X = 2n-1, then the set of comultiplications of X is in one-one correspondence with $Ext^{n-1}(A, A ⊗ A)$. Then the case $G = ℤ_{p^k}$ leads to an example of infinitely many G-homotopically distinct G-maps $φ_i : X → Y$ such that $φ_i^H$, $φ_j^H : X^H → Y^H$ are homotopic for all i,j and all subgroups H ⊆ G.

LA - eng

KW - homotopy classes of comultiplications; Moore -space

UR - http://eudml.org/doc/212051

ER -

## References

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