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Abstract

Imitating the classical q-expansion principle we use the elliptic character map to develop the relation between elements in elliptic cohomology and their q-series in K-theory. We show that, under certain exactness conditions, the integrality of elliptic objects is completely controlled by their characters.

As an application, we obtain an interpretation of the cooperations in elliptic cohomology as was conjectured by F. Clarke and K. Johnson. It enables us to give a description of the elliptic based Adams-Novikov spectral sequence in terms of cyclic cohomology of modular forms in several variables, and to set up a higher e-invariant with values in N. Katz's ring of divided congruences.

We show how the topological q-expansion principle can be used to equip elliptic cohomology with orientations which obey various Riemann-Roch formulas. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)

Details

Title
The topological q-expansion principle
Author
Laures, Gerd
Year
1996
Publisher
ProQuest Dissertations & Theses
Source type
Dissertation or Thesis
Language of publication
English
ProQuest document ID
304309443
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.