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Analytic torsion and R-torsion of Riemannian manifolds.(English)Zbl 0395.57011


MSC:

57Q10 Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc.
53C20 Global Riemannian geometry, including pinching
57R05 Triangulating
58A99 General theory of differentiable manifolds
58J99 Partial differential equations on manifolds; differential operators

Citations:

Zbl 0358.57005

Cite

References:

[1]Agmon, S., Lectures on Elliptic Boundary Value Problems, (Mathematical Studies (1965), Van Nostrand: Van Nostrand Princeton, N.J.), No. 2 ·Zbl 0109.32701
[2]Agmon, S.; Douglis, A.; Nirenberg, L., Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, II, Comm. Pure Appl. Math., 17, 35-92 (1964) ·Zbl 0123.28706
[3]Atiyah, M. F.; Patodi, V. K.; Singer, I. M., Spectral asymmetry and Riemannian geometry, I, (Proc. Cambridge Philos. Soc., 77 (1975)), 43-69 ·Zbl 0297.58008
[4]Colin de Verdière, Y., Propriétés asymptotiques de l’équation de la chaleur sur une variété compacte, (Séminaire Bourbaki, Vol. 1973/74 (1975), Springer: Springer Berlin/Heidelberg/New York), 58-68, Lecture Notes in Mathematics, No. 431 ·Zbl 0324.58019
[5]Conner, P. E., The Neumann’s Problem for Differential Forms on Riemannian Manifolds, (Mem. Amer. Math. Soc., Vol. 20 (1956), Amer. Math. Soc.,: Amer. Math. Soc., Providence, R.I.) ·Zbl 0070.31404
[6]Dodziuk, J., Finite-difference approach to the Hodge theory of harmonic forms, Amer. J. Math., 98, 79-104 (1976) ·Zbl 0324.58001
[7]J. Dodziuk and V. K. Patodi;J. Dodziuk and V. K. Patodi ·Zbl 0435.58004
[8]Friedman, A., Partial Differential Equations of Parabolic Type (1964), Prentice-Hall: Prentice-Hall Englewood Cliffs, N.J. ·Zbl 0144.34903
[9]Hurwitz, A.; Courant, R., Vorlesungen über allgemeine Funktionentheorie und elliptische Funktionen (1964), Springer: Springer Berlin/Heidelberg/New York ·Zbl 0135.12101
[10]Kato, T., Pertubation Theory for Linear Operators (1966), Springer: Springer Berlin/Heidelberg/New York ·Zbl 0148.12601
[11]Kwun, K. W.; Szcarba, R. H., Product and sum theorems for Whitehead torsion, Ann. of Math., 82, 183-190 (1965) ·Zbl 0142.40703
[12]Lions, J. L.; Magenes, E., (Non-homogeneous Boundary Value Problems, Vol. I (1970), Springer: Springer Berlin/Heidelberg/New York) ·Zbl 0197.06701
[13]Milnor, J. W., Whitehead torsion, Bull. Amer. Math. Soc., 72, 358-426 (1966) ·Zbl 0147.23104
[14]Milnor, J. W., A duality theorem for Reidemeister torsion, Ann. of Math., 76, 137-147 (1962) ·Zbl 0108.36502
[15]Morrey, C. B., A variational method in the theory of harmonic integrals, II, Amer. J. Math., 78, 137-170 (1956) ·Zbl 0070.31402
[16]Munkres, J. R., Elementary Differential Topology, (Ann of Math. Studies No. 54 (1966), Princeton Univ. Press: Princeton Univ. Press Princeton, N.J.) ·Zbl 0107.17201
[17]de Neymet de Christ, S., Some relations in Whitehead torsion, Bull. Soc. Mat. Mexicana, 12, 2, 55-70 (1967), (in Spanish) ·Zbl 0182.57202
[18]Patodi, V. K., Riemannian structures and triangulation of manifolds, (Proceedings of the International Congress of Mathematicians. Proceedings of the International Congress of Mathematicians, Vancouver (1974)) ·Zbl 0333.57008
[19]Ray, D. B.; Singer, I. M., \(R\)-Torsion and the Laplacian on Riemannian manifolds, Advances in Math., 7, 145-210 (1971) ·Zbl 0239.58014
[20]Ray, D. B., Reidemeister torsion and the Laplacian on lens spaces, Advances in Math., 4, 109-126 (1970) ·Zbl 0204.23804
[21]Seeley, R., Complex powers of an elliptic operator, (Proc. Symp. Pure Math.. Proc. Symp. Pure Math., Chicago, 1966. Proc. Symp. Pure Math.. Proc. Symp. Pure Math., Chicago, 1966, Singular Integrals (1967), Amer. Math. Soc.,: Amer. Math. Soc., Providence, R.I.), 288-307 ·Zbl 0159.15504
[22]Seeley, R., Analytic extension of the trace associated with elliptic boundary problems, Amer. J. Math., 91, 963-983 (1969) ·Zbl 0191.11901
[23]Taylor, M. E., Pseudo Differential Operators, (Lecture Notes in Mathematics, No. 416 (1974), Springer: Springer Berlin/Heidelberg/New York) ·Zbl 0207.45402
[24]Whitney, H., Geometric Integration Theory (1957), Princeton Univ. Press: Princeton Univ. Press Princeton, N.J. ·Zbl 0083.28204
[25]Cheeger, J., Analytic torsion and Reidemeister torsion, (Proc. Nat. Acad. Sci. USA, 74 (1977)), 2651-2654 ·Zbl 0358.57005
[26]J. Cheeger;J. Cheeger ·Zbl 0412.58026
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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