Relative $K$-cycles and elliptic boundary conditions

Guihua Gong

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arXiv · math/9301213

Relative $K$-cycles and elliptic boundary conditions

Guihua Gong

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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 $\p M$, $D$ 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 $\dim(M)$ $\not=$ 4, 5, 6, 7 and the ``only if'' part of the conjecture for arbitrary dimension.

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Guihua Gong. 1993-01-01. Relative $K$-cycles and elliptic boundary conditions. https://arxiv.org/abs/math/9301213

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