Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-28T05:51:59.476Z Has data issue: false hasContentIssue false
  • English
  • Français

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., leticia@math.cinvestav.mx.
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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