Harmonic Spinors for Twisted Dirac Operators

Details Harmonic Spinors for Twisted Dirac Operators Harmonic Spinors for Twisted Dirac Operators

1997-06-27

arxiv.org/abs/dg-ga/9706016v1

Math. Ann. 309, 225-246 (1997)

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, uses pstricks macro-package, 27 pages with 4 figures, to appear in Math. Ann

Scientific paper

We show that for a suitable class of ``Dirac-like'' operators there holds a Gluing Theorem for connected sums. More precisely, if $M_1$ and $M_2$ are closed Riemannian manifolds of dimension $n\ge 3$ together with such operators, then the connected sum $M_1 # M_2$ can be given a Riemannian metric such that the spectrum of its associated operator is close to the disjoint union of the spectra of the two original operators. As an application, we show that in dimension $n\equiv 3$ mod 4 harmonic spinors for the Dirac operator of a spin, $\Spinc$, or $\Spinh$ manifold are not topologically obstructed.

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