Complex cobordism and embeddability of CR-manifolds
نویسندگان
چکیده
منابع مشابه
Complex cobordism and embeddability of CR-manifolds
This paper studies complex cobordisms between compact, three dimensional, strictly pseudoconvex Cauchy-Riemann manifolds. Suppose the complex cobordism is given by a complex 2-manifold X with one pseudoconvex and one pseudoconcave end. We answer the following questions. To what extent is X determined by the pseudoconvex end? What is the relation between the embeddability of the pseudoconvex end...
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We obtain an embedding theorem for compact strongly pseudoconvex CR manifolds which are bounadries of some complete Hermitian manifolds. We use this to compactify some negatively curved Kähler manifolds with compact strongly pseudoconvex boundary. An embedding theorem for Sasakian manifolds is also derived.
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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...
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Two notions of cobordism are defined for compact CR-manifolds. The weaker notion, complex cobordism realizes two CR-manifolds as the boundary of a complex manifold; in the stronger notion, strict complex cobordism there is a strictly plurisubharmonic function defined on the total space of the cobordism with the boundary components as level sets of this function. We show that embeddability for a...
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This paper is a continuation of the ongoing study of cobordism of Grassmann manifolds. Let F denote one of the division rings R of reals, C of complex numbers, or H of quaternions. Let t = dimRF . Then the Grassmannian manifold Gk(F) is defined to be the set of all k-dimensional (left) subspaces of Fn+k. Gk(F) is a closed manifold of real dimension nkt. Using the orthogonal complement of a subs...
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ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2003
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2003.v10.n5.a12