Relative -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 , *D* possesses an elliptic boundary condition if and only if in , where [*D*] is the relative *K*-cycle in corresponding to *D*. We prove the "if" part of this conjecture for and the "only if" part of the conjecture for arbitrary dimension.

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DOI:
https://doi.org/10.1090/S0273-0979-1993-00349-5

Article copyright:
© Copyright 1993
American Mathematical Society