The spinorial $\tau$-invariant and 0-dimensional surgery
type: Dataset
description: Let $M$ be a compact manifold with a metric $g$ and with a fixed spin structure $\chi$. Let $\lambda_1^+(g)$ be the first non-negative eigenvalue of the Dirac operator on $(M,g,\chi)$. We set $$\tau(M,\chi):= \sup \inf \lambda_1^+(g)$$ 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 $(M^\#,\chi^\#)$ be obtained from $(M,\chi)$ by $0$-dimensional surgery. We prove that $$\tau(M^\#,\chi^\#)\geq \tau(M,\chi).$$ As a corollary we can calculate $\tau(M,\chi)$ for any Riemann surface $M$.
issued: 2026-05-09T03:49:53.890027
language: en
modified: 2026-05-09T03:49:53.890032
contact point: Organization
  fn: CCSD
keyword: 53c27-primary-58j05-57r65-secondary
keyword: conformal-geometry
keyword: dirac-operators
keyword: gluing-formula
keyword: infoeu-reposemanticspreprint
keyword: mathmath-dgmathematics-mathdifferential-geometry-mathdg
keyword: preprints-working-papers-
landing page: https://hal.science/hal-00087981

The spinorial $\tau$-invariant and 0-dimensional surgery
type: Distribution
format: HTML
issued: 2026-05-09T03:49:53.891860
modified: 2026-05-09T03:49:53.880260
access URL: https://hal.science/hal-00087981

test_moissonnage_selune
type: Agent