no. G11
Article de recherche - Géométrie et Topologie
K-cowaist of manifolds with boundary
[K-cowaist des variétés à bord]
Bär, Christian1  ; Hanke, Bernhard2
1Universität Potsdam, Institut für Mathematik, 14476 Potsdam, Germany
2Universität Augsburg, Institut für Mathematik, 86135 Augsburg, Germany
Comptes Rendus. Mathématique, Tome 362 (2024) no. G11, pp. 1349-1356

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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Révisé le :
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DOI : 10.5802/crmath.646
Classification : 53C21, 53C23, 53C27, 58J20
Keywords: Manifolds with boundary, lower scalar curvature bounds, lower mean curvature bounds, Atiyah–Patodi–Singer index formula, $K$-cowaist, $\omega $-cowaist
Mots-clés : Variétés à bord, minorations de la courbure scalaire, minorations de la courbure moyenne, le théorème de l’indice d’Atiyah–Patodi–Singer, $K$-cowaist, $\omega $-cowaist

Bär, Christian  1   ; Hanke, Bernhard  2

1 Universität Potsdam, Institut für Mathematik, 14476 Potsdam, Germany
2 Universität Augsburg, Institut für Mathematik, 86135 Augsburg, Germany
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     title = {\protect\emph{K}-cowaist of manifolds with boundary},
     journal = {Comptes Rendus. Math\'ematique},
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     year = {2024},
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Bär, Christian; Hanke, Bernhard. K-cowaist of manifolds with boundary. Comptes Rendus. Mathématique, Tome 362 (2024) no. G11, pp. 1349-1356. doi: 10.5802/crmath.646

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

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

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

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

[6] Gromov, Mikhael; Lawson, H. Blaine Jr 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] Gromov, Mikhael Four lectures on scalar curvature, Perspectives in scalar curvature. Vol. 1, World Scientific, 2023, pp. 1-514 | DOI | MR | Zbl

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

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

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

[12] Wang, Xiangsheng 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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