Rationality of renormalized Chern classes
- Authors
- Burns, D.; Ryu, J. -S.
- Issue Date
- 2005
- Publisher
- INT PRESS BOSTON, INC
- Citation
- PURE AND APPLIED MATHEMATICS QUARTERLY, v.1, no.3, pp.449 - 478
- Journal Title
- PURE AND APPLIED MATHEMATICS QUARTERLY
- Volume
- 1
- Number
- 3
- Start Page
- 449
- End Page
- 478
- URI
- https://scholarworks.bwise.kr/hongik/handle/2020.sw.hongik/25237
- ISSN
- 1558-8599
- Abstract
- Renormalized Chern classes (c) over tilde (2),...,(c) over tilde (n) for a compact, connected, complex manifold X with smooth, strictly pseudoconvex boundary M were defined in [7]. A Chern-Simons type invariant was also defined in [6] for a compact, strictly pseudoconvex CR-manifold M of dimension three, and a Gauss-Bonnet theorem relating the two in [7]. We show here that if M is spherical, and P((c) over tilde (2),...(c) over tilde (n)) is a polynomial with rational coefficients in (c) over tilde (2),...(c) over tilde (n), then the corresponding Chern class P(X) = P((c) over tilde (2),...,(c) over tilde (n)) defines a class in H* (X, M; Q). The proof is based on the multi-valued Hartogs theorem of [5] and the exponents of monodromy for a development map.
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