Bibliographic Details
| Title: |
MoravaK-theories of classifying spaces and generalized characters for groups |
| Authors: |
Michael J. Hopkins, Nicholas J. Kuhn, Douglas C. Ravenel |
| Contributors: |
The Pennsylvania State University CiteSeerX Archives |
| Superior Title: |
http://www.math.rochester.edu/people/faculty/doug/mypapers/barc.pdf. |
| Publisher Information: |
Springer |
| Publication Year: |
1992 |
| Collection: |
CiteSeerX |
| Subject Terms: |
4 Counting the orbits in Gn, p 12 |
| Description: |
This paper is intended to be an informal introduction to [HKR], where we study the Morava K–theories (which will be partially defined below) of the classifying space of a finite group G and related matters. It will be long on exposition and short on proofs, in the spirit of the third author’s lecture at the conference. In Section 1 we will recall Atiyah’s theorem relating the complex K–theory of BG to the complex representation ring R(G). We will also define classical characters on G. In Section 2 we will introduce the Morava K–theories K(n)∗ and the related theories E(n)∗. In Section 3 we will state our main results and conjectures. Most of the former are generalizations of the classical results stated in Section 1. In the remaining five sections we will outline the proofs of our results. Section 4 is purely group–theoretic, i.e., it makes no use of any topology. In it we will prove our formula for the number χn,p(G) of conjugacy classes of commuting n– tuples of elements of prime power order in a finite group G. We have discussed this material with several prominent group theorists, but we have yet to find one who admits to ever having considered this question. In Section 5 we equate this number with the Euler characteristic of K(n)∗(BG). Our generalized characters are functions on the set of such conjugacy classes with values in certain p–adic fields. In Section 6 we recall the Lubin–Tate construction from local algebraic num-ber theory. It uses formal group laws to construct abelian extensions of finite extensions of the field of p–adic numbers. We need it in Section 7 where we describe the connection between E(n)∗(BG) and our generalized characters. In Section 8, we prove a theorem about wreath products. A corollary of this is that our main conjecture (3.5) about K(n)∗(BG) holds for all the symmetric ∗Partially supported by the National Science Foundation †Partially supported by the NSF, the Sloan Foundation and the SERC ‡Partially supported by the NSF 1 groups. |
| Document Type: |
text |
| File Description: |
application/pdf |
| Language: |
English |
| Relation: |
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.558.3261; http://www.math.rochester.edu/people/faculty/doug/mypapers/barc.pdf |
| Availability: |
http://www.math.rochester.edu/people/faculty/doug/mypapers/barc.pdf |
| Rights: |
Metadata may be used without restrictions as long as the oai identifier remains attached to it. |
| Accession Number: |
edsbas.69A3A7D8 |
| Database: |
BASE |
