A comparison of norm maps
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- by Anna Marie Bohmann; with an appendix by Anna Marie Bohmann; with an appendix by Emily Riehl PDF
- Proc. Amer. Math. Soc. 142 (2014), 1413-1423 Request permission
Abstract:
We present a spectrum-level version of the norm map in equivariant homotopy theory based on the algebraic construction in the 1997 paper by Greenlees and May. We show that this new norm map is the same as the construction in the 2009 paper by Hill, Hopkins and Ravenel. Our comparison of the two norm maps gives a conceptual understanding of the choices inherent in the definition of the multiplicative norm map.References
- Leonard Evens, The cohomology of groups, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1991. Oxford Science Publications. MR 1144017
- J. P. C. Greenlees and J. P. May, Localization and completion theorems for $M\textrm {U}$-module spectra, Ann. of Math. (2) 146 (1997), no. 3, 509–544. MR 1491447, DOI 10.2307/2952455
- Michael A. Hill, Michael J. Hopkins, and Douglas C. Ravenel, On the non-existence of elements of Kervaire invariant one (2009), arXiv:0908.3724v2 [math.AT].
- Peter T. Johnstone, Sketches of an elephant: a topos theory compendium. Vol. 1, Oxford Logic Guides, vol. 43, The Clarendon Press, Oxford University Press, New York, 2002. MR 1953060
- Jacob Lurie, Higher topos theory, Annals of Mathematics Studies, vol. 170, Princeton University Press, Princeton, NJ, 2009. MR 2522659, DOI 10.1515/9781400830558
- Saunders Mac Lane and Ieke Moerdijk, Sheaves in geometry and logic, Universitext, Springer-Verlag, New York, 1994. A first introduction to topos theory; Corrected reprint of the 1992 edition. MR 1300636
- M. A. Mandell and J. P. May, Equivariant orthogonal spectra and $S$-modules, Mem. Amer. Math. Soc. 159 (2002), no. 755, x+108. MR 1922205, DOI 10.1090/memo/0755
Additional Information
- Anna Marie Bohmann
- Affiliation: Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, Illinois 60637
- Address at time of publication: Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, Illinois 60208
- Email: bohmann@math.northwestern.edu
- Emily Riehl
- Affiliation: Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, Illinois 60637
- Address at time of publication: Department of Mathematics, Harvard University, One Oxford Street, Cambridge, Massachusetts 02138
- Email: eriehl@math.harvard.edu
- Received by editor(s): January 27, 2012
- Received by editor(s) in revised form: April 30, 2012
- Published electronically: January 8, 2014
- Additional Notes: The first author thanks MSRI for hosting the Hot Topics: Kervaire Invariant workshop of October 2010, which inspired this research.
The second author was supported by an NSF graduate research fellowship and by an NSF Mathematical Sciences Postdoctoral Research Fellowship - Communicated by: Brooke Shipley
- © Copyright 2014 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 142 (2014), 1413-1423
- MSC (2010): Primary 55P91, 55P42; Secondary 18D30
- DOI: https://doi.org/10.1090/S0002-9939-2014-11845-4
- MathSciNet review: 3162261