Abstract
Renormalized Chern classes ~2;:::;~n for a compact, connected, complex manifold X with smooth, strictly pseudoconvex boundary M were deflned in (7). A Chern-Simons type invariant was also deflned 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(~c2;:::;~n) is a polynomial with rational coe-cients in ~2;:::;~n, then the corresponding Chern class P(X) = P(~c2;:::;~n) deflnes 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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