A -equivariant analog of Mahowald's Thom spectrum theorem
Authors:
Mark Behrens and Dylan Wilson
Journal:
Proc. Amer. Math. Soc. 146 (2018), 5003-5012
MSC (2010):
Primary 55P91, 55S91
DOI:
https://doi.org/10.1090/proc/14175
Published electronically:
August 14, 2018
MathSciNet review:
3856165
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We prove that the -equivariant Eilenberg-MacLane spectrum associated with the constant Mackey functor
is equivalent to a Thom spectrum over
.
- [AB14] O. Antolín-Camarena and T. Barthel, A simple universal property of Thom ring spectra, ArXiv e-prints (2014).
- [Ati68] M. F. Atiyah, Bott periodicity and the index of elliptic operators, Quart. J. Math. Oxford Ser. (2) 19 (1968), 113–140. MR 228000, https://doi.org/10.1093/qmath/19.1.113
- [BH15] Andrew J. Blumberg and Michael A. Hill, Operadic multiplications in equivariant spectra, norms, and transfers, Adv. Math. 285 (2015), 658–708. MR 3406512, https://doi.org/10.1016/j.aim.2015.07.013
- [GM95] J. P. C. Greenlees and J. P. May, Generalized Tate cohomology, Mem. Amer. Math. Soc. 113 (1995), no. 543, viii+178. MR 1230773, https://doi.org/10.1090/memo/0543
- [GM17] Bertrand J. Guillou and J. Peter May, Equivariant iterated loop space theory and permutative 𝐺-categories, Algebr. Geom. Topol. 17 (2017), no. 6, 3259–3339. MR 3709647, https://doi.org/10.2140/agt.2017.17.3259
- [Hil17] Michael A. Hill, On algebras over equivariant little disks, arXiv:1709.02005, 2017.
- [HK01] Po Hu and Igor Kriz, Real-oriented homotopy theory and an analogue of the Adams-Novikov spectral sequence, Topology 40 (2001), no. 2, 317–399. MR 1808224, https://doi.org/10.1016/S0040-9383(99)00065-8
- [HM17] Michael A. Hill and Lennart Meier, The 𝐶₂-spectrum 𝑇𝑚𝑓₁(3) and its invertible modules, Algebr. Geom. Topol. 17 (2017), no. 4, 1953–2011. MR 3685599, https://doi.org/10.2140/agt.2017.17.1953
- [LMSM86] L. G. Lewis Jr., J. P. May, M. Steinberger, and J. E. McClure, Equivariant stable homotopy theory, Lecture Notes in Mathematics, vol. 1213, Springer-Verlag, Berlin, 1986. With contributions by J. E. McClure. MR 866482
- [Mah77] Mark Mahowald, A new infinite family in ₂𝜋_{*}^{𝑠}, Topology 16 (1977), no. 3, 249–256. MR 445498, https://doi.org/10.1016/0040-9383(77)90005-2
- [May96] J. P. May, Equivariant homotopy and cohomology theory, CBMS Regional Conference Series in Mathematics, vol. 91, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1996. With contributions by M. Cole, G. Comezaña, S. Costenoble, A. D. Elmendorf, J. P. C. Greenlees, L. G. Lewis, Jr., R. J. Piacenza, G. Triantafillou, and S. Waner. MR 1413302
- [RS00] Colin Rourke and Brian Sanderson, Equivariant configuration spaces, J. London Math. Soc. (2) 62 (2000), no. 2, 544–552. MR 1783643, https://doi.org/10.1112/S0024610700001241
- [Ull13] John Ullman, Tambara functors and commutative ring spectra, arXiv:1304.4912v2, 2013.
- [Wil17]
Dylan Wilson, Power operations for
and a cellular construction of
, arXiv:1611.06958v2, 2017.
Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 55P91, 55S91
Retrieve articles in all journals with MSC (2010): 55P91, 55S91
Additional Information
Mark Behrens
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, Indiana
Email:
mbehren1@nd.edu
Dylan Wilson
Affiliation:
Department of Mathematics, 5734 S. University Avenue, Chicago, Illinois 60637
Email:
dwilson@math.uchicago.edu
DOI:
https://doi.org/10.1090/proc/14175
Received by editor(s):
August 23, 2017
Received by editor(s) in revised form:
February 3, 2018
Published electronically:
August 14, 2018
Additional Notes:
The first author was supported by NSF grant DMS-1611786.
Communicated by:
Michael A. Mandell
Article copyright:
© Copyright 2018
American Mathematical Society