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- Volume 362 (2024)

- p. 1349-1356

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We extend the K-cowaist inequality to generalized Dirac operators in the sense of Gromov and Lawson and study applications to manifolds with boundary.

Nous étendons l’inégalité de K-cowaist aux opérateurs de Dirac généralisés au sens de Gromov et Lawson et étudions les applications aux variétés à bord.

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Christian Bär 1 ; Bernhard Hanke 2

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[1] M. F. Atiyah; V. K. Patodi; I. M. Singer Spectral asymmetry and Riemannian geometry. I, Math. Proc. Camb. Philos. Soc., Volume 77 (1975), pp. 43-69 | DOI | MR | Zbl

[2] M. F. Atiyah K-theory. With notes by D. W. Anderson, Advanced Book Classics, Addison-Wesley Publishing Company, 1989, xx+216 pages | MR | Zbl

[3] Christian Bär; Werner Ballmann Guide to elliptic boundary value problems for Dirac-type operators, Arbeitstagung Bonn 2013 (Progress in Mathematics), Volume 319, Birkhäuser/Springer, 2016, pp. 43-80 | DOI | MR | Zbl

[4] Christian Bär; Bernhard Hanke Boundary conditions for scalar curvature, Perspectives in scalar curvature. Vol. 2, World Scientific, 2023, pp. 325-377 | DOI | MR | Zbl

[5] Yoshiyasu Fukumoto Invariance of finiteness of K-area under surgery, Geom. Dedicata, Volume 176 (2015), pp. 175-183 | DOI | MR | Zbl

[6] Mikhael Gromov; H. Blaine Lawson Positive scalar curvature and the Dirac operator on complete Riemannian manifolds, Publ. Math., Inst. Hautes Étud. Sci., Volume 58 (1983), pp. 83-196 | DOI | MR | Zbl | Numdam

[7] Mikhael Gromov Four lectures on scalar curvature, Perspectives in scalar curvature. Vol. 1, World Scientific, 2023, pp. 1-514 | DOI | MR | Zbl

[8] Mikhael Gromov Positive curvature, macroscopic dimension, spectral gaps and higher signatures, Functional analysis on the eve of the 21st century, Vol. II (New Brunswick, NJ, 1993) (Progress in Mathematics), Volume 132, Birkhäuser, 1996, pp. 1-213 | DOI | MR | Zbl

[9] Benedikt Hunger Almost flat bundles and homological invariance of infinite K-area, New York J. Math., Volume 25 (2019), pp. 687-722 | MR | Zbl

[10] Mario Listing Homology of finite K-area, Math. Z., Volume 275 (2013) no. 1-2, pp. 91-107 | Zbl | DOI | MR

[11] H. Blaine Lawson; Marie-Louise Michelsohn Spin geometry, Princeton Mathematical Series, 38, Princeton University Press, 1989, xii+427 pages | MR | Zbl

[12] Xiangsheng Wang On a relation between the K-cowaist and the A ^-cowaist, Proc. Am. Math. Soc., Volume 151 (2023) no. 11, pp. 4983-4990 | DOI | MR | Zbl

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