The spinorial τ-invariant and 0-dimensional surgery


Let M be a compact manifold with a metric g and with a fixed spin structure χ. Let be the first non-negative eigenvalue of the Dirac operator on (M,g,χ).

We set

where the infimum runs over all metrics g of volume 1 in a conformal class [g0] on M and where the supremum runs over all conformal classes [g0] on M.

Let be obtained from (M,χ) by 0-dimensional surgery. We prove that


As a corollary we can calculate τ(M,χ) for any Riemann surface M.

If the inline PDF is not rendering correctly, you can download the PDF file here.


Journal + Issues

The Journal für die reine und angewandte Mathematik is the oldest mathematics periodical still in existence. Founded in 1826 by August Leopold Crelle and edited by him until his death in 1855, it soon became widely known under the name of Crelle’s Journal. In the 190 years of its existence, Crelle’s Journal has developed to an outstanding scholarly periodical with one of the worldwide largest circulations among mathematics journals.