正标量曲率与同调协不变量

Pub Date : 2023-05-29 DOI:10.1112/topo.12299

Hokuto Konno, Masaki Taniguchi

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引用次数: 0

摘要

利用Seiberg-Witten理论中的同调协不变量，给出了4‐流形上具有S1×S3$S^{1} \乘以S^{3}$的正标量曲率度量的阻碍。证明的主要工具是周期端4流形上的一个相对Bauer-Furuta型不变量。

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Positive scalar curvature and homology cobordism invariants

We give an obstruction to positive scalar curvature metrics on 4-manifolds with the homology $S^{1} \times S^{3}$ described in terms of homology cobordism invariants from Seiberg–Witten theory. The main tool of the proof is a relative Bauer–Furuta-type invariant on a periodic-end 4-manifold.

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