Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Interpreting the Bökstedt smash product as the norm

Authors: Vigleik Angeltveit, Andrew J. Blumberg, Teena Gerhardt, Michael A. Hill and Tyler Lawson
Journal: Proc. Amer. Math. Soc. 144 (2016), 5419-5433
MSC (2010): Primary 55P91
Published electronically: June 17, 2016
MathSciNet review: 3556283
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: This paper compares two models of the equivariant homotopy type of the smash powers of a spectrum, namely the ``Bökstedt smash product'' and the Hill-Hopkins-Ravenel norm.

References [Enhancements On Off] (What's this?)

  • [1] Andrew J. Blumberg and Michael A. Mandell, The homotopy theory of cyclotomic spectra, Geom. Topol. 19 (2015), no. 6, 3105-3147. MR 3447100,
  • [2] Andrew J. Blumberg, Continuous functors as a model for the equivariant stable homotopy category, Algebr. Geom. Topol. 6 (2006), 2257-2295. MR 2286026,
  • [3] M. Bökstedt,
    Topological Hochschild homology,
  • [4] M. Bökstedt, W. C. Hsiang, and I. Madsen, The cyclotomic trace and algebraic $ K$-theory of spaces, Invent. Math. 111 (1993), no. 3, 465-539. MR 1202133,
  • [5] Bjørn Ian Dundas, Relative $ K$-theory and topological cyclic homology, Acta Math. 179 (1997), no. 2, 223-242. MR 1607556,
  • [6] Wojciech Chachólski and Jérôme Scherer, Homotopy theory of diagrams, Mem. Amer. Math. Soc. 155 (2002), no. 736, x+90. MR 1879153,
  • [7] A. D. Elmendorf, I. Kriz, M. A. Mandell, and J. P. May, Rings, modules, and algebras in stable homotopy theory, Mathematical Surveys and Monographs, vol. 47, American Mathematical Society, Providence, RI, 1997. With an appendix by M. Cole. MR 1417719
  • [8] Thomas G. Goodwillie, Relative algebraic $ K$-theory and cyclic homology, Ann. of Math. (2) 124 (1986), no. 2, 347-402. MR 855300,
  • [9] Lars Hesselholt and Ib Madsen, On the $ K$-theory of finite algebras over Witt vectors of perfect fields, Topology 36 (1997), no. 1, 29-101. MR 1410465,
  • [10] M. A. Hill, M. J. Hopkins, and D. C. Ravenel,
    On the non-existence of elements of Kervaire invariant one,
    Preprint, arXiv:0908.3724.
  • [11] John A. Lind, Diagram spaces, diagram spectra and spectra of units, Algebr. Geom. Topol. 13 (2013), no. 4, 1857-1935. MR 3073903,
  • [12] Sverre Lunøe-Nielsen and John Rognes, The topological Singer construction, Doc. Math. 17 (2012), 861-909. MR 3007679
  • [13] Ib Madsen, Algebraic $ K$-theory and traces, Current developments in mathematics, 1995 (Cambridge, MA), Int. Press, Cambridge, MA, 1994, pp. 191-321. MR 1474979
  • [14] 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,
  • [15] M. A. Mandell, J. P. May, S. Schwede, and B. Shipley, Model categories of diagram spectra, Proc. London Math. Soc. (3) 82 (2001), no. 2, 441-512. MR 1806878,
  • [16] M. A. Mandell and B. Shipley, A telescope comparison lemma for THH, Topology Appl. 117 (2002), no. 2, 161-174. MR 1875908,
  • [17] Randy McCarthy, Relative algebraic $ K$-theory and topological cyclic homology, Acta Math. 179 (1997), no. 2, 197-222. MR 1607555,
  • [18] Christian Schlichtkrull, Units of ring spectra and their traces in algebraic $ K$-theory, Geom. Topol. 8 (2004), 645-673 (electronic). MR 2057776,
  • [19] Brooke Shipley, Symmetric spectra and topological Hochschild homology, $ K$-Theory 19 (2000), no. 2, 155-183. MR 1740756,
  • [20] R. Villarroel-Flores,
    The action by natural transformations of a group on a diagram of spaces,
    Preprint, 0411502.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 55P91

Retrieve articles in all journals with MSC (2010): 55P91

Additional Information

Vigleik Angeltveit
Affiliation: Department of Mathematics, Australian National University, Canberra, ACT 0200, Australia

Andrew J. Blumberg
Affiliation: Department of Mathematics, University of Texas, Austin, Texas 78712

Teena Gerhardt
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824

Michael A. Hill
Affiliation: Department of Mathematics, University of California Los Angeles, Los Angeles, California 90095

Tyler Lawson
Affiliation: Department of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455

Received by editor(s): November 12, 2015
Received by editor(s) in revised form: February 8, 2016
Published electronically: June 17, 2016
Additional Notes: The first author was supported in part by an NSF All-Institutes Postdoctoral Fellowship administered by the Mathematical Sciences Research Institute through its core grant DMS-0441170, NSF grant DMS-0805917, and an Australian Research Council Discovery Grant
The second author was supported in part by NSF grant DMS-0906105
The third author was supported in part by NSF DMS–1007083 and NSF DMS–1149408
The fourth author was supported in part by NSF DMS–0906285, DARPA FA9550-07-1-0555, and the Sloan Foundation
The fifth author was supported in part by NSF DMS–1206008 and the Sloan Foundation.
Communicated by: Michael A. Mandell
Article copyright: © Copyright 2016 by the authors

American Mathematical Society