Topological Characterization of Contractible 3-Manifolds with Positive Scalar Curvature

Wang, Jian

doi:10.1142/9789811273230_0009

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Appendix a µ-Bubbles1

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2023

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“…In particular, S 1 admits a PSC metric, and rS 1 s ‰ 0 P H 3 pM, Zq. Since π 2 pM q is trivial, the topological classification of closed 3-manifolds admitting a PSC metric implies that S 1 is homologous to a spherical class in H 3 pM, Zq (see [Wan19,p. 112]).…”

Section: Appendix a µ-Bubblesmentioning

confidence: 99%

Rigidity and non-rigidity of $\H^n/\Z^{n-2}$ with scalar curvature bounded from below

Hao¹,

Hu²,

Liu³

et al. 2023

Preprint

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We show that the hyperbolic manifold H n {Z n´2 is not rigid under all compactly supported deformations that preserve the scalar curvature lower bound ´npn ´1q, and that it is rigid under deformations that are further constrained by certain topological conditions. In addition, we prove two related splitting results. Contents 1. Introduction 1 2. Non-rigidity of H n {Z n´2 5 3. ALH manifolds, mass and deformations 10 4. Two rigidity results 17 5. Two splitting results of 'cuspidal-boundary' type 20 Appendix A. µ-bubbles 24 Appendix B. Topological lemmas 26 Acknowledgement 28 References 28

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Section: Appendix a µ-Bubblesmentioning

confidence: 99%