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1994-1995 | 146 | 1 | 59-67
Tytuł artykułu

Co-H-structures on equivariant Moore spaces

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Rocznik
Tom
146
Numer
1
Strony
59-67
Opis fizyczny
Daty
wydano
1994
otrzymano
1993-07-27
poprawiono
1994-01-21
Twórcy
  • Department of Mathematics, Dartmouth College, Hanover, New Hampshire 03755, U.S.A.
  • Faculty of Mathematics and Informatics, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
Bibliografia
  • [A-G] M. Arkowitz and M. Golasiński, Co-H-structures on Moore spaces of type (A, 2), Canad. J. Math., to appear.
  • [Br] G. E. Bredon, Equivariant Cohomology Theories, Lecture Notes in Math. 34, Springer, 1967.
  • [Ca] G. Carlsson, A counterexample to a conjecture of Steenrod, Invent. Math. 64 (1981), 171-174.
  • [Co] S. R. Costenoble and S. Waner, A nonexistence result for Moore G-spectra, Proc. Amer. Math. Soc. 113 (1991), 265-274.
  • [Do1] R. Doman, Non-G-equivalent Moore G-spaces of the same type, ibid. 103 (1988), 1317-1321.
  • [Do2] R. Doman, Moore G-spaces which are not co-Hopf G-spaces, Canad. Math. Bull. 32 (1989), 365-368.
  • [D-D-K] E. Dror, Dwyer and D. M. Kan, Equivariant maps which are self homotopy equivalences, Proc. Amer. Math. Soc. 80 (1980), 670-672.
  • [El] A. D. Elmendorf, Systems of fixed point sets, Trans. Amer. Math. Soc. 277 (1983), 275-284.
  • [Il1] S. Illman, Equivariant algebraic topology, Ph. D. Thesis, Princeton University, Princeton, N.J., 1972.
  • [Il2] S. Illman, Equivariant singular homology and cohomology I, Mem. Amer. Math. Soc. 156 (1975).
  • [Ka1] P. J. Kahn, Rational Moore G-spaces, Trans. Amer. Math. Soc. 298 (1986), 245-271.
  • [Ka2] P. J. Kahn, Equivariant homology decompositions, ibid., 273-287.
  • [Ka3] P. J. Kahn, Steenrod's problem and k-invariants of certain classifying spaces, in: Algebraic K-Theory, Lecture Notes in Math. 967, Springer, 1982, 195-214.
  • [Ma] T. Matumoto, On G-CW complexes and a theorem of J. H. C. Whitehead, J. Fac. Sci. Univ. Tokyo 18 (1971), 363-374.
  • [M-T] R. E. Mosher and M. C. Tangora, Cohomology Operations and Applications in Homotopy Theory, Harper & Row, New York, 1968.
  • [Qu] D. G. Quillen, Homotopical Algebra, Lecture Notes in Math. 43, Springer, 1967.
  • [Sm] J. R. Smith, Equivariant Moore spaces II - The low dimensional case, J. Pure Appl. Algebra 36 (1985), 187-204.
  • [Tr] G. V. Triantafillou, Rationalization of Hopf G-spaces, Math. Z. 182 (1983), 485-500.
  • [Un] H. Unsöld, Topological minimal algebras and Sullivan-de Rham equivalence, Astérisque 113-114 (1984), 337-343.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv146i1p59bwm
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