Loop Groups and Their Flag Varieties

A pr 2 00 8 TWISTED LOOP GROUPS AND THEIR AFFINE FLAG VARIETIES

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Complex cobordism of Hilbert manifolds with some applications to flag varieties of loop groups

We develop a version of Quillen’s geometric cobordism theory for infinite dimensional separable Hilbert manifolds. This cobordism theory has a graded group structure under the topological union operation and has pushforward maps for Fredholm maps. We discuss transverse approximations and products, and the contravariant property of this cobordism theory. We define Euler classes for finite dimens...

Complex cobordism of Hilbert manifolds

Slide 2 We will define a notion of cobordism generalizing that of Quillen: • D. G. Quillen, Elementary proofs of some results of cobordism theory using Steenrod operations, Adv. in Math. 7 (1971), 29–56. Details appear in • C. Özel, On the Complex Cobordism of Flag Varieties Associated to Loop Groups, PhD thesis, University of Glasgow (1998). • A. Baker & C. Özel, Complex cobordism of Hilbert m...

Geometry of Loop Eisenstein Series

Part 3. Geometric Construction of Loop Eisenstein Series 31 11. Bloch’s Map 31 12. Adeleic Loop groups and G-bundles on a Punctured Surface 33 13. Affine flag varieties and extensions of G-bundles 38 14. Relative Chern classes and Central extensions 41 15. Loop Eisenstein Series and Geometric Generating Functions 47 16. Ribbons and a Formal Analogue 48 17. Example: Loop Eisenstein Series on P1. 53