Abstract:For every closed surface of genus at least $3$, equipped with any bounding spin structure, we show that the index difference, viewed as a map from the fundamental group of the space of Dirac-invertible Riemannian metrics to $\KO^{-4}(*)$, is non-trivial. If the genus is at least $5$, we also show that the aforementioned index difference is surjective. For products of two closed surfaces of genus at least $3$, equipped with any spin structure, we prove that the corresponding space of Dirac-invertible Riemannian metrics is not contractible. We discuss the relationship of this result to the existence of metrics with harmonic spinors in dimension~$4$.
From: Samuel Lockman [view email]
[v1]
Wed, 10 Jun 2026 16:21:03 UTC (18 KB)
[v2]
Fri, 7 Aug 2026 08:17:22 UTC (24 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。