The $3$-local $tmf$-homology of $B\Sigma _3$
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- by Michael A. Hill PDF
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Abstract:
In this paper, we introduce a Hopf algebra, developed by the author and André Henriques, which is usable in the computation of the $tmf$-homology of a space. As an application, we compute the $tmf$-homology of $B\Sigma _3$ in a manner analogous to Mahowald and Milgram’s computation of the $ko$-homology $\mathbb RP^{\infty }$.References
- Greg Arone and Mark Mahowald, The Goodwillie tower of the identity functor and the unstable periodic homotopy of spheres, Invent. Math. 135 (1999), no. 3, 743–788. MR 1669268, DOI 10.1007/s002220050300
- Andrew Baker and Andrej Lazarev, On the Adams spectral sequence for $R$-modules, http://hopf.math.purdue.edu/Baker-Lazarev/Rmod-ASS.pdf.
- Tilman Bauer, Computation of the homotopy of the spectrum $tmf$, arXiv:math.AT/0311328.
- Mark Behrens, A modular description of the $K(2)$-local sphere at the prime 3, Topology 45 (2006), no. 2, 343–402. MR 2193339, DOI 10.1016/j.top.2005.08.005
- Armand Borel, Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts, Ann. of Math. (2) 57 (1953), 115–207 (French). MR 51508, DOI 10.2307/1969728
- J. P. C. Greenlees and J. P. May, Generalized Tate cohomology, Mem. Amer. Math. Soc. 113 (1995), no. 543, viii+178. MR 1230773, DOI 10.1090/memo/0543
- M. Mahowald and R. James Milgram, Operations which detect Sq4 in connective $K$-theory and their applications, Quart. J. Math. Oxford Ser. (2) 27 (1976), no. 108, 415–432. MR 433453, DOI 10.1093/qmath/27.4.415
- Mark Mahowald, A new infinite family in ${}_{2}\pi _{*}{}^s$, Topology 16 (1977), no. 3, 249–256. MR 445498, DOI 10.1016/0040-9383(77)90005-2
- Mark Mahowald, The image of $J$ in the $EHP$ sequence, Ann. of Math. (2) 116 (1982), no. 1, 65–112. MR 662118, DOI 10.2307/2007048
- Norihiko Minami, On the odd-primary Adams $2$-line elements, Topology Appl. 101 (2000), no. 3, 231–255. MR 1733806, DOI 10.1016/S0166-8641(98)00122-9
- Charles Rezk, Supplementary notes for math $512$, www.math.uiuc.edu/ rezk/papers.html.
Additional Information
- Michael A. Hill
- Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
- Address at time of publication: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22903
- MR Author ID: 822452
- ORCID: 0000-0001-8125-8107
- Email: mikehill@virginia.edu
- Received by editor(s): July 17, 2006
- Received by editor(s) in revised form: September 13, 2006
- Published electronically: August 14, 2007
- Communicated by: Paul Goerss
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 4075-4086
- MSC (2000): Primary 55N34; Secondary 55T15
- DOI: https://doi.org/10.1090/S0002-9939-07-08937-X
- MathSciNet review: 2341960