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Forum Mathematicum

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π(L2T(1)/(v1)) and its applications in computing π(L2T(1)) at the prime two

Citation Information: Forum Mathematicum. Volume 19, Issue 1, Pages 127–147, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: 10.1515/FORUM.2007.006, February 2007

Publication History

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In this paper, all spaces are localized at the prime two. Let T(1) be the Ravenel spectrum characterized by the BP -homology as BP [t 1], T(1)/(v 1) be the cofiber of the self map v 1 : Σ2 T(1) → T(1) and L 2 denote the Bousfield localization functor with respect to v 2 −1 BP . In this paper, we compute the homotopy groups π(L 2 T(1)/(v 1)) by determining the E -term of its Adams-Novikov spectral sequence (ANSS). From the E 2-term of the ANSS for π(L 2 T(1)/(v 1)), we determine a subgroup of the E 2-term for π(L 2 T(1)). We also show that the E 4-term for π(L 2 T(1)) has horizontal vanishing line.

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