ar X iv : m at h / 06 07 71 6 v 1 [ m at h . D G ] 2 7 Ju l 2 00 6 THE SPINORIAL τ - INVARIANT AND 0 - DIMENSIONAL SURGERY
نویسندگان
چکیده
Let M be a compact manifold with a metric g and with a fixed spin structure χ. Let λ + 1 (g) be the first non-negative eigenvalue of the Dirac operator on (M, g, χ). We set τ (M, χ) := sup inf λ + 1 (g) where the infimum runs over all metrics g of volume 1 in a conformal class [g 0 ] on M and where the supremum runs over all conformal classes [g 0 ] on M. Let (M # , χ #) be obtained from (M, χ) by 0-dimensional surgery. We prove that τ (M # , χ #) ≥ τ (M, χ). As a corollary we can calculate τ (M, χ) for any Riemann surface M .
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