The Dirac operator on collapsing S 1 -bundles
Séminaire de théorie spectrale et géométrie, Tome 16 (1997-1998), pp. 33-42.
@article{TSG_1997-1998__16__33_0,
     author = {Ammann, Bernd},
     title = {The {Dirac} operator on collapsing $S^1$-bundles},
     journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie},
     pages = {33--42},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {16},
     year = {1997-1998},
     zbl = {0935.58014},
     language = {en},
     url = {http://www.numdam.org/item/TSG_1997-1998__16__33_0/}
}
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Ammann, Bernd. The Dirac operator on collapsing $S^1$-bundles. Séminaire de théorie spectrale et géométrie, Tome 16 (1997-1998), pp. 33-42. http://www.numdam.org/item/TSG_1997-1998__16__33_0/

[1] I. Agricola, B. Ammann, T. Friedrich, A comparison of the eigenvalues of the Dirac and Laplace operator on the two-dimensional torus. Preprint 1998. | Zbl 0944.58022

[2] B. Ammann, Spin-Strukturen und das Spektrum des Dirac-Operators, Dissertation, Universität Freiburg, ISBN 3-8265-4282-7, Shaker Verlag Aachen 1998.

[3] B. Ammann, C. Bär, The Dirac Operator on Nilmanifolds and Collapsing Circle Bundles, Ann. Global Anal. Geom. 16, 221-253 ( 1998). | MR 1626659 | Zbl 0911.58037

[4] C. Bär, Metrics with harmonic spinors, GAFA 6, 899-942 ( 1996). | MR 1421872 | Zbl 0867.53037

[5] L. Bérard Bergery, J.-P. Bourguignon, Riemannian submersions with totally geodesic fibers, Illinois J. Math. 26, 151-200 ( 1982). | MR 650387 | Zbl 0483.58021

[6] B. Colbois, G. Courtois, Convergence de variétés et convergence du spectre du Laplacien, Ann. Sc. Ec. Norm. Sup. 4e série 24, 507-518 ( 1991). | Numdam | MR 1123559 | Zbl 0754.58040

[7] B. Colbois, J. Dodziuk, Riemannian metrics with large λ1, Proc. Amer. Math. Soc. 122 no. 3, 905-906 ( 1994). | MR 1213857 | Zbl 0820.58056

[8] T. Friedrich, Zur Abhängigkeit des Dirac-Operators von der Spin-Strukturt, Colloq. Math. 48, 57-62 ( 1984). | MR 750754 | Zbl 0542.53026

[9] K. Fukaya, Collapsing of Riemannian manifolds and eigenvalues of Laplace operator, Invent. Math. 87, 517-547 ( 1987). | MR 874035 | Zbl 0589.58034

[10] P.B. Gilkey, J.H. Park, Eigenvalues of the Laplacian and Riemannian submersions,Yokohama Math. J. 43 no. 1, 7-11 ( 1995). | MR 1363013 | Zbl 0853.58107

[11] P.B. Gilkey, J.H. Park, Riemannian submersions which preserve the eigenforms of the Laplacian, III. J. Math. 40, 194-201 ( 1996). | MR 1398089 | Zbl 0855.58059

[12] P.B. Gilkey, J.V. Leahy, J.H. Park, Eigenvalues of the form valued Laplacian for Riemannian submersions, Proc. Amer. Math. Soc. 126 no. 6,1845-1850 ( 1998). | MR 1485476 | Zbl 0903.58061

[13] N. Hitchin, Harmonic spinors, Adv. Math. 14, 1-55 ( 1974). | MR 358873 | Zbl 0284.58016

[14] J.-Y. Wu, The topological spectrum of a smooth closed manifold, Ind. Univ. Math. J.44, no. 2, 511-534 ( 1995). | MR 1355410 | Zbl 0843.58124