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On the BP-homology of 2e × 2e

Published online by Cambridge University Press:  23 July 2008

Leticia Zárate
Leticia Zárate
Affiliation:
Departamento de Matemáticas, Centro de Investigación y de Estudios Avanzados del IPN, Apartado Postal 14–740, 07000 México City, D.F., [email protected].
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Abstract

We study υ0- and υ1-divisibility properties of the [2e]-series associated to the universal 2-typical formal group law. This allows us to identify elements annihilating the toral class τ in BP*(2e × 2e). We conjecture that these elements form a minimal system of generators of the annihilator ideal of τ. This would provide a Landweber-type presentation for the BP-homology of 2e × 2e from which the relation hom:dimBP (Z2e × Z2e) = 2 would be an easy consequence.

Keywords

2-typical [2e]-seriesConner-Floyd conjecture
Type
Research Article
Information
Journal of K-Theory , Volume 3 , Issue 3 , June 2009 , pp. 409 - 435
Copyright
Copyright © ISOPP 2009

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References

1.Araki, S.: Typical formal groups in complex cobordism and K-theory, Lectures in Math., Kyoto Univ., Kinokuniya, 6, 1973Google Scholar
2.Conner, P. E. and Floyd, E. E.. Differentiable Periodic Maps, Academic Press Inc., New York; Springer-Verlag, Berlin-Goettingen-Heidelberg, 1964Google Scholar
3.Floyd, E.: Actions of (Zp)k without stationary points, Topology 10 (1971), 327–336CrossRefGoogle Scholar
4.González, J.: 2-divisibility in the Brown-Peterson [2k]-series, J. Pure Appl. Algebra 157 (1) (2001), 57–68CrossRefGoogle Scholar
5.Johnson, D. C. and Wilson, W. S.: The Brown-Peterson homology of elementary p-groups, Amer. J. Math. 107 (2) (1985), 427–453CrossRefGoogle Scholar
6.Johnson, D. C. and Wilson, W. S.: Projective dimension and Brown-Peterson homology, Topology 12 (1973), 327–353CrossRefGoogle Scholar
7.Landweber, P. S.: Künneth formulas for bordism theories, Trans. Amer. Math. Soc. 121 (1966), 242–256Google Scholar
8.Mitchell, S.: A proof of the Conner-Floyd conjecture, Amer. J. Math. 106 (4) (1984), 889–891CrossRefGoogle Scholar
9.Nakos, G.: On ideals annihilating the toral class of BP*((BZ/pk)n), Canad. Math. Bull. 36 (3) (1993), 332–343CrossRefGoogle Scholar
10.Nakos, G.: On the Brown-Peterson homology of certain classifying spaces, Ph.D. Thesis, The Johns Hopkins University, 1985Google Scholar
11.Ravenel, D. C. and Wilson, W. S.: The Morava K-theories of Eilenberg-Mac Lane spaces and the Conner-Floyd conjecture, Amer. J. Math. 102 (4) (1980), 691–748CrossRefGoogle Scholar
12.Dieck, T. tom: Actions of finite abelian p-groups without stationary points, Topology 9 (1970), 359–366CrossRefGoogle Scholar
13.Zárate, L.: On the BP 〈n〉*-homomology of 2e × 2e, Ph.D. Thesis, CINVESTAV – IPN, 2007Google Scholar