Relative $K$-cycles and elliptic boundary conditions
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- by Guihua Gong PDF
- Bull. Amer. Math. Soc. 28 (1993), 104-108 Request permission
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.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Bull. Amer. Math. Soc. 28 (1993), 104-108
- MSC: Primary 58G12; Secondary 19K33, 46L99
- DOI: https://doi.org/10.1090/S0273-0979-1993-00349-5
- MathSciNet review: 1168515