K-cowaist on complete foliated manifolds

Su, Guangxiang; Wang, Xiangsheng

doi:10.2140/agt.2025.25.2037

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ISSN (electronic): 1472-2739

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$\mathrm{K}$-cowaist on complete foliated manifolds

Guangxiang Su and Xiangsheng Wang

Algebraic & Geometric Topology 25 (2025) 2037–2052

DOI: 10.2140/agt.2025.25.2037

Abstract

Let $(M, F)$ be a connected (not necessarily compact) foliated manifold carrying a complete Riemannian metric $g^{T M}$ . We generalize Gromov’s $K$ -cowaist using the coverings of $M$ , as well as defining a closely related concept called the $\hat{A}$ -cowaist. Let $k^{F}$ be the associated leafwise scalar curvature of $g^{F} = g^{T M} |_{F}$ . We obtain some estimates on $k^{F}$ using these two concepts. In particular, assuming that the generalized $K$ -cowaist is infinity and either $T M$ or $F$ is spin, we show that $\inf (k^{F}) \leq 0$ .

Keywords

scalar curvature, foliation, K-cowaist

Mathematical Subject Classification

Primary: 58J20

Secondary: 53C12, 53C21

References

Publication

Received: 22 June 2022

Accepted: 5 June 2024

Published: 11 August 2025

Authors

Guangxiang Su
Chern Institute of Mathematics & LPMC Nankai University Tianjin China

Xiangsheng Wang
School of Mathematics Shandong University Jinan China

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Volume 25, issue 4 (2025)