On Fredholm index, transversal approximations and Quillen's geometric complex cobordism of Hilbert manifolds with some applications to flag varieties of loop groups
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Dosyalar
Tarih
2006
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Dergi Başlığı
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Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
In [Contemp. Math. 258 (2000) 1-19], by using Fredholm index we developed a version of Quillen's geometric cobordism theory for infinite dimensional Hilbert manifolds. This cobordism theory has a graded group structure under topological union operation and has push-forward maps for complex orientable Fredholm maps. In this work, by using Quinn's Transversality Theorem [Proc. Sympos. Pure. Math. 15 (1970) 213-222], it will be shown that this cobordism theory has a graded ring structure under transversal intersection operation and has pull-back maps for smooth maps. It will be shown that the Thom isomorphism in this theory will be satisfied for finite dimensional vector bundles over separable Hilbert manifolds and the projection formula for Gysin maps will be proved. After we discuss the relation between this theory and classical cobordism, we describe some applications to the complex cobordism of flag varieties of loop groups and we do some calculations. © 2005 Elsevier B.V. All rights reserved.
Açıklama
Anahtar Kelimeler
Cobordism, Flag Variety, Fredholm Map, Hilbert Manifold, Loop Group, Transversal Approximations
Kaynak
Topology and its Applications
WoS Q Değeri
Q3
Scopus Q Değeri
Q3
Cilt
153
Sayı
9
