On the gluing problem for the $\eta$-invariant
Ulrich Bunke
Source: J. Differential Geom. Volume 41, Number 2
(1995), 397-448.
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Mathematical Reviews number (MathSciNet): MR1331973
Zentralblatt MATH identifier: 0821.58037
References
[1] M. F. Atiyah, V. K. Patodi and I. M. Singer, Spectral asymmetry and Riemannian geometry, Math. Proc. Cambridge Philos. Soc. 77 (1975) 43-69.
Zentralblatt MATH: 0297.58008
Mathematical Reviews (MathSciNet): MR397797
Digital Object Identifier: doi:10.1017/S0305004100049410
[2] J. E. Avron, R. Seiler and B. Simon, The quantum Hall effect and the relative index for projections, preprint, TU-Berlin, no. 262, 1990.
[3] J. E. Avron, R. Seiler and B. Simon, The quantum Hall effect and the relative index for projections, preprint, SFB 288, No. 56, 1993.
[4] N. Berline, E. Getzler and M. Vergne, Heat kernels and Dirac operators, Springer, Berlin, 1992.
Zentralblatt MATH: 0744.58001
Mathematical Reviews (MathSciNet): MR1215720
[5] J. M. Bismut and J. Cheeger, Remarks on the families index theorem for manifolds with boundary, Differential Geometry (B. Lawson and K. Tenenblat, eds.), Pitman Monographs Surveys Pure Appl. Math., Longman Scientific and Technical, 1991.
Mathematical Reviews (MathSciNet): MR1173033
Zentralblatt MATH: 0727.58045
[6] J. M. Bismut and D. S. Freed, The analysis of elliptic families, Comm.Math. Phys. 107 (1986) 103-163.
Zentralblatt MATH: 0657.58038
Mathematical Reviews (MathSciNet): MR861886
Digital Object Identifier: doi:10.1007/BF01206955
Project Euclid: euclid.cmp/1104115934
[7] B. B. Boo-Bavnbek and K. P. Wojciechowski, Elliptic boundary problems for Dirac operators, Birkhauser, Basel, 1993.
Zentralblatt MATH: 0797.58004
Mathematical Reviews (MathSciNet): MR1233386
[8] T. Branson and P. Gilkey, Residues of the -functionfor an operator of Dirac type, J. Functional Analysis 108 (1992) 47-87.
Zentralblatt MATH: 0756.58048
Mathematical Reviews (MathSciNet): MR1174158
Digital Object Identifier: doi:10.1016/0022-1236(92)90146-A
[9] K. S. Brown, Cohomology of groups, Springer, Berlin, 1982.
Zentralblatt MATH: 0584.20036
Mathematical Reviews (MathSciNet): MR672956
[10] U. Bunke, Comparison of Dirac operators on manifolds with boundary, Rend. Circ. Mat. Palermo (Suppl.) 30 (1993) 133-141.
Zentralblatt MATH: 0797.58084
Mathematical Reviews (MathSciNet): MR1246627
[11] U. Bunke, On the spectral flow of families of Dirac operators with constant symbol, Math. Nachr. 165 (1994) 191-203.
Zentralblatt MATH: 0834.58037
Mathematical Reviews (MathSciNet): MR1261370
Digital Object Identifier: doi:10.1002/mana.19941650113
[12] U. Bunke, A K-theoreticrelativeindex theorem and Callias-type Dirac operators, to appear in Math. Ann..
Zentralblatt MATH: 0835.58035
Mathematical Reviews (MathSciNet): MR1348799
Digital Object Identifier: doi:10.1007/BF01460989
[13] U. Bunke, -invariants for manifolds with boundary, preprint SFB 288, No. 52, 1993.
[14] U. Bunke, A glueing formula for the eta-invariant, preprint SFB 288, No. 58, 1993.
[15] U. Bunke, Splitting the spectral flow, preprint SFB 288, no. 63, 1993.
[16] U. Bunke, The -invariant as a Lagrangian of a topological quantum field theory, preprint SFB 288, no. 93.
[17] S. Cappell, R. Lee and E. Miller, preprint.
[18] S. Cappell, R. Lee and E. Miller, On the Maslov index, preprint.
Zentralblatt MATH: 0805.58022
Mathematical Reviews (MathSciNet): MR1263126
Digital Object Identifier: doi:10.1002/cpa.3160470202
[19] J. Cheeger, Spectral geometry of singular Riemannian spaces, J. Differential Geometry 18 (1983) 575-657.
Zentralblatt MATH: 0529.58034
Mathematical Reviews (MathSciNet): MR730920
Project Euclid: euclid.jdg/1214438175
[20] J. Cheeger, -Invariants, the adiabatic approximation and conical singularities, J. Differential Geometry 26 (1987) 175-221.
Zentralblatt MATH: 0623.58021
Mathematical Reviews (MathSciNet): MR892036
Project Euclid: euclid.jdg/1214441181
[21] J. Cheeger, M. Gromov and M. Taylor, Finite propagation speed, kernel estimates for functions of the Laplace operatorand the geometry of completeRiemannian manifolds, J. Differential Geometry 17 (1982) 15-53.
Zentralblatt MATH: 0493.53035
Mathematical Reviews (MathSciNet): MR658471
Project Euclid: euclid.jdg/1214436699
[22] P. Chernoff, Essential selfadjointness of powers of generators of hyperbolic equations, J. FunctionalAnalysis 12 (1973) 401-414.
Zentralblatt MATH: 0263.35066
Mathematical Reviews (MathSciNet): MR369890
Digital Object Identifier: doi:10.1016/0022-1236(73)90003-7
[23] A. Connes, The Chern character in K-homology, Inst. Hautes Etudes Sci. Publ. Math. 54 (1984) 1-69.
[24] R. D. Douglas and K. P. Wojciechowski, Adiabatic limits of the -invariants, the odd dimensional Atiyah-Patodi-Singer problem, Comm.Math. Phys. 142 (1991) 139-168.
Zentralblatt MATH: 0746.58074
Mathematical Reviews (MathSciNet): MR1137777
Digital Object Identifier: doi:10.1007/BF02099174
Project Euclid: euclid.cmp/1104248492
[25] P. B. Gilkey, Invariance theory, the heat equation, and the Atiyah-Singer index theorem, Publish or Perish, Wilmington, 1984.
Zentralblatt MATH: 0565.58035
Mathematical Reviews (MathSciNet): MR783634
[26] M. Gromov and H. B. Lawson, Positive scalar curvature and the Dirac operatoron complete Riemannian manifolds, Inst.HautesEtudes Sci. Publ.Math. 58 (1983) 295-408.
Zentralblatt MATH: 0538.53047
[27] V. Guillemin and S. Steinberg, Geometric asymptotic, Math. Surveys, No. 14, Amer. Math. Soc, Providence, RI, 1977. T. Kato, Perturbation theoryfor linear operators, Springer, Berlin, 1980.
Zentralblatt MATH: 0364.53011
[29] P. Kirk and E. Klassen, Computing spectral flow via cup products, J. Differential Geometry 40 (1994) 505-562.
Zentralblatt MATH: 0816.58038
Mathematical Reviews (MathSciNet): MR1305980
Project Euclid: euclid.jdg/1214455777
[30] H. B. Lawson and M. L. Michelsohn, Spin geometry, Princeton, NJ, 1989.
Zentralblatt MATH: 0688.57001
[31] M. Lesch and K. P. Wojciechowski, The -invariant of generalized Atiyah-Patodi-Singer boundary value problems: dependence of on the boundary condition and a generator of -el(d)), Preprint, 1993.
Zentralblatt MATH: 0866.58054
Mathematical Reviews (MathSciNet): MR1386311
Project Euclid: euclid.ijm/1255986187
[32] G. Lion and M. Vergne, The Weil representation, Maslov index and theta series, Birkhauser, Boston and Basel, 1980.
Zentralblatt MATH: 0444.22005
Mathematical Reviews (MathSciNet): MR573448
[33] R. R. Mazzeo and R. B. Melrose, Analytic surgery and the -invariant, preprint, 1992.
Zentralblatt MATH: 0838.57022
[34] R. Meyerhoff and D. Ruberman, Cutting and pasting the -invariant, Duke Math. J. 61 (1990) 747-761.
Zentralblatt MATH: 0739.57008
Mathematical Reviews (MathSciNet): MR1084457
Digital Object Identifier: doi:10.1215/S0012-7094-90-06127-7
Project Euclid: euclid.dmj/1077296991
[35] R. Meyerhoff and D. Ruberman, Mutation and the -invariant, J. Differential Geometry 31 (1990) 101-130.
Zentralblatt MATH: 0689.57012
Mathematical Reviews (MathSciNet): MR1030667
Project Euclid: euclid.jdg/1214444091
[36] W. Mller, -invariants and manifolds with boundary, J. Differential Geometry 40 (1994) 311-377.
Zentralblatt MATH: 0817.53025
Mathematical Reviews (MathSciNet): MR1293657
Project Euclid: euclid.jdg/1214455539
[37] L. I. Nicolaescu, The Maslov index, the spectral flow and splittings of manifolds, preprint, 1993.
Zentralblatt MATH: 0780.58021
Mathematical Reviews (MathSciNet): MR1239040
[38] E. H. Spanier, algebraic topology, McGraw-Hill, New York, 1966.
Zentralblatt MATH: 0145.43303
Mathematical Reviews (MathSciNet): MR210112
[39] C. T. C. Wall, Non-additivity of the signature, Invent. Math. 7 (1969) 269-274.
Zentralblatt MATH: 0176.21501
Mathematical Reviews (MathSciNet): MR246311
Digital Object Identifier: doi:10.1007/BF01404310
[40] K. P. Wojciechowski, On the additivity of the -invariant, preprint, 1993.
Zentralblatt MATH: 0816.58036
[41] T. Yoshida, Floer homology and splittings of manifolds, Ann. of Math. (2) 134 (1991) 277-323.
Zentralblatt MATH: 0748.57002
Mathematical Reviews (MathSciNet): MR1127477
Digital Object Identifier: doi:10.2307/2944348
JSTOR: links.jstor.org
Journal of Differential Geometry
