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MULTIPLICATIVE ORIENTATIONS OF KO-THEORY AND OF THE SPECTRUM OF TOPOLOGICAL MODULAR FORMS
 

Summary: MULTIPLICATIVE ORIENTATIONS OF KO-THEORY AND OF THE SPECTRUM OF
TOPOLOGICAL MODULAR FORMS
MATTHEW ANDO, MICHAEL J. HOPKINS, AND CHARLES REZK
Abstract. We describe the space of E spin orientations of KO and the space of E string orientations
of tmf.
Contents
1. Introduction 1
2. Units of ring spectra and the space of orientations 4
3. Rational orientations and characteristic classes 8
4. Localization of units 13
5. String orientations 16
6. String orientations of KO 21
7. String orientations of KOp 21
8. Proof of Theorem 6.1 25
9. Maps between p-adic K-theory spectra 26
10. Bernoulli numbers, Eisenstein series, and the Mazur measure 29
11. K(n) localizations of tmf 36
12. String orientations of tmf: statement of main results 38
13. First reductions 38
14. Orientations of LK(1)tmf 40

  

Source: Ando, Matthew - Department of Mathematics, University of Illinois at Urbana-Champaign

 

Collections: Mathematics