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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

Relative $ K$-cycles and elliptic boundary conditions


Author: Guihua Gong
Journal: Bull. Amer. Math. Soc. 28 (1993), 104-108
MSC: Primary 58G12; Secondary 19K33, 46L99
MathSciNet review: 1168515
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Abstract: In this paper, we discuss the following conjecture raised by Baum-Douglas: For any first-order elliptic differential operator D on smooth manifold M with boundary $ \partial M$, D possesses an elliptic boundary condition if and only if $ \partial [D] = 0$ in $ {K_1}(\partial M)$, where [D] is the relative K-cycle in $ {K_0}(M,\partial M)$ corresponding to D. We prove the "if" part of this conjecture for $ dim(M) \ne 4,5,6,7$ and the "only if" part of the conjecture for arbitrary dimension.


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DOI: http://dx.doi.org/10.1090/S0273-0979-1993-00349-5
PII: S 0273-0979(1993)00349-5
Article copyright: © Copyright 1993 American Mathematical Society