Geodesic
K-cowaist on complete foliated manifolds
Su, Guangxiang1 ; Wang, Xiangsheng2
1Chern Institute of Mathematics & LPMC, Nankai University, Tianjin, China
2School of Mathematics, Shandong University, Jinan, China
Algebraic and Geometric Topology, Tome 25 (2025) no. 4, pp. 2037-2052
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Let (M,F) be a connected (not necessarily compact) foliated manifold carrying a complete Riemannian metric gTM. We generalize Gromov’s K ⁡ -cowaist using the coverings of M, as well as defining a closely related concept called the A ⁡ ^-cowaist. Let kF be the associated leafwise scalar curvature of gF = gTM|F. We obtain some estimates on kF using these two concepts. In particular, assuming that the generalized K ⁡ -cowaist is infinity and either TM or F is spin, we show that inf ⁡ (kF) ≤ 0.

DOI : 10.2140/agt.2025.25.2037
Keywords: scalar curvature, foliation, K-cowaist

Su, Guangxiang  1   ; Wang, Xiangsheng  2

1 Chern Institute of Mathematics & LPMC, Nankai University, Tianjin, China
2 School of Mathematics, Shandong University, Jinan, China 
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Su, Guangxiang; Wang, Xiangsheng. K-cowaist on complete foliated manifolds. Algebraic and Geometric Topology, Tome 25 (2025) no. 4, pp. 2037-2052. doi: 10.2140/agt.2025.25.2037

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