On the Morava K-theory of 
Author:
Björn Schuster
Journal:
Proc. Amer. Math. Soc. 142 (2014), 1437-1445
MSC (2010):
Primary 55R35, 55N20; Secondary 57T25
DOI:
https://doi.org/10.1090/S0002-9939-2014-11873-9
Published electronically:
January 27, 2014
MathSciNet review:
3162263
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We show that for all 
and all primes 
, the Morava K-theory of the classifying space of the Mathieu group 
is generated by transfers of Euler classes.
- [1] Malkhaz Bakuradze and Vladimir Vershinin, Morava 𝐾-theory rings for the dihedral, semidihedral and generalized quaternion groups in Chern classes, Proc. Amer. Math. Soc. 134 (2006), no. 12, 3707–3714. MR 2240687, https://doi.org/10.1090/S0002-9939-06-08424-3
- [2] Michael J. Hopkins, Nicholas J. Kuhn, and Douglas C. Ravenel, Generalized group characters and complex oriented cohomology theories, J. Amer. Math. Soc. 13 (2000), no. 3, 553–594. MR 1758754, https://doi.org/10.1090/S0894-0347-00-00332-5
- [3] John Hunton, The Morava 𝐾-theories of wreath products, Math. Proc. Cambridge Philos. Soc. 107 (1990), no. 2, 309–318. MR 1027783, https://doi.org/10.1017/S0305004100068572
- [4] Igor Kriz, Morava 𝐾-theory of classifying spaces: some calculations, Topology 36 (1997), no. 6, 1247–1273. MR 1452850, https://doi.org/10.1016/S0040-9383(96)00049-3
- [5] Carlos Prieto, Transfer and the spectral sequence of a fibration, Trans. Amer. Math. Soc. 271 (1982), no. 1, 133–142. MR 648082, https://doi.org/10.1090/S0002-9947-1982-0648082-X
- [6] Daniel Quillen, Elementary proofs of some results of cobordism theory using Steenrod operations, Advances in Math. 7 (1971), 29–56 (1971). MR 0290382, https://doi.org/10.1016/0001-8708(71)90041-7
- [7] Björn Schuster, On the Morava 𝐾-theory of some finite 2-groups, Math. Proc. Cambridge Philos. Soc. 121 (1997), no. 1, 7–13. MR 1418356, https://doi.org/10.1017/S0305004196001156
- [8] Björn Schuster, 𝐾(𝑛) Chern approximations of some finite groups, Algebr. Geom. Topol. 12 (2012), no. 3, 1695–1720. MR 2966700, https://doi.org/10.2140/agt.2012.12.1695
- [9] Björn Schuster, Morava 𝐾-theory of groups of order 32, Algebr. Geom. Topol. 11 (2011), no. 1, 503–521. MR 2783236, https://doi.org/10.2140/agt.2011.11.503
- [10] Björn Schuster and Nobuaki Yagita, Morava 𝐾-theory of extraspecial 2-groups, Proc. Amer. Math. Soc. 132 (2004), no. 4, 1229–1239. MR 2045443, https://doi.org/10.1090/S0002-9939-03-07183-1
-theory rings for the dihedral, semidihedral and generalized quaternion groups in Chern classes, Proc. Amer. Math. Soc. 134 (2006), no. 12, 3707-3714. 
-theories of wreath products, Math. Proc. Cambridge Philos. Soc. 107 (1990), no. 2, 309-318. 
-theory of classifying spaces: some calculations, Topology 36 (1997), no. 6, 1247-1273. 
-theory of some finite 
-groups, Math. Proc. Cambridge Philos. Soc. 121 (1997), no. 1, 7-13. 
Chern approximations of some finite groups, Algebr. Geom. Topol. 12 (2012), no. 3, 1695-1720. 
-theory of groups of order 32, Algebr. Geom. Topol. 11 (2011), no. 1, 503-521. 
-theory of extraspecial 2-groups, Proc. Amer. Math. Soc. 132 (2004), no. 4, 1229-1239 (electronic). Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 55R35, 55N20, 57T25
Retrieve articles in all journals with MSC (2010): 55R35, 55N20, 57T25
Additional Information
Björn Schuster
Affiliation:
FB C Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, Wuppertal, Germany
Address at time of publication:
Fakultät für Mathematik, Ruhr-Universität Bochum, 44801 Bochum, Germany
Email:
bjoern.schuster@rub.de
DOI:
https://doi.org/10.1090/S0002-9939-2014-11873-9
Received by editor(s):
September 8, 2010
Received by editor(s) in revised form:
May 10, 2012
Published electronically:
January 27, 2014
Communicated by:
Brooke Shipley
Article copyright:
© Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
