The 5–local homotopy of eo4

Hill, Michael A

doi:10.2140/agt.2008.8.1741

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The $5$–local homotopy of $eo_4$

Michael A Hill

Algebraic & Geometric Topology 8 (2008) 1741–1761

DOI: 10.2140/agt.2008.8.1741

Abstract

We compute the cohomology of a $5$ –local analogue of the Weierstrass Hopf algebroid used to compute $t m f$ –homology. We also compute the Adams–Novikov differentials for various stages, finding the homotopy, $V (0)$ –homology and $V (1)$ –homology of the putative spectrum $e o_{4}$ . We also link this computation to the homotopy of the higher real $K$ –theory spectrum $E O_{4}$ .

Keywords

Bockstein, K-theory, Hopkins–Miller

Mathematical Subject Classification 2000

Primary: 55T25, 18G40, 55N35

Secondary: 55Q51, 18G60

References

Publication

Received: 18 August 2008

Revised: 29 August 2008

Accepted: 1 September 2008

Published: 9 October 2008

Authors

Michael A Hill
Department of Mathematics University of Virginia PO Box 400137 Charlottesville, VA 22904 USA
http://people.virginia.edu/~mah7cd

Volume 8, issue 3 (2008)