Geometric heat kernel coefficient for APS-type boundary conditions
Journées équations aux dérivées partielles (1998), article no. 11, 19 p.

I present an alternative way of computing the index of a Dirac operator on a manifold with boundary and a special family of pseudodifferential boundary conditions. The local version of this index theorem contains a number of divergence terms in the interior, which are higher order heat kernel invariants. I will present a way of associating boundary terms to those divergence terms, which are rather local of nature.

@article{JEDP_1998____A11_0,
     author = {Salomonsen, Gorm},
     title = {Geometric heat kernel coefficient for {APS-type} boundary conditions},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {11},
     publisher = {Universit\'e de Nantes},
     year = {1998},
     zbl = {01808720},
     mrnumber = {99h:58180},
     language = {en},
     url = {http://www.numdam.org/item/JEDP_1998____A11_0/}
}
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Salomonsen, Gorm. Geometric heat kernel coefficient for APS-type boundary conditions. Journées équations aux dérivées partielles (1998), article  no. 11, 19 p. http://www.numdam.org/item/JEDP_1998____A11_0/

[APS] Atiyah, M.F., Patodi, V.K., Singer, I.M. : «Spectral Asymmetry and Riemannian Geometry I.», Math. Proc. Cambridge Philos. Soc. 77 (1975), 43-69. | MR | Zbl

[BGV] Berline, N., Getzler, E., Vergne, M. : «Heat Kernels and Dirac Operators», Second Edition, Springer-Verlag (1996).

[BW] Boos, B., Wojciechowski, K. : «Elliptic Boundary Problems for Dirac Operators», Birkhauser, Boston (1993).

[Ca1] Carron, G. : « Inégalités de Sobolev et L2-Cohomologie », Séminaire de Théorie Spectrale et Géométrie GRENOBLE 1994-1995 (171-176) | Numdam | MR | Zbl

[Ca2] Carron, G. : « Un Théorème de L'Indice Relativ. » Séminaire de théorie Spectrale et Géométrie GRENOBLE 1996-1997 (193-202) | Numdam | Zbl

[Ca3] Carron, G. : « Théorèmes de L'Indice sur les Variétés Non-Compactes » Preprint, April 1998. | Zbl

[Ch] Chernoff, P.R. : «Essential Self-adjointness of Powers of Generators of Hyperbolic Equations.» J. Funct. Anal. 12 (1973), 401-414. | MR | Zbl

[Gi] Gilkey, P. : «Invariance Theory, the Heat Equation and the Atiyah-Patodi-Singer Index Theorem», 2nd edition, CRC Press (1995) | MR | Zbl

[Gr1] Grubb, G. «Heat Trace Expansions for Elliptic Systems with Pseudodifferential Boundary Conditions.» Preprint, University of Copenhagen, November 1997.

[Gr2] Grubb, G. «Functional Calculus of Pseudodifferential Boundary problems» Birkhäuser, Boston (1986). | MR | Zbl

[GS] Grubb, G., Seeley, R. : «Weakly Parametric Pseudodifferential Operators and Atiyah-Patodi-Singer Boundary Problems.», Invent. Math. 121 (1995) 481-529. | MR | Zbl

[Gy] Gray, A. : «Tubes.» Addison-Wesley, New York, 1990 | MR | Zbl

[HMM] Hassel, A., Mazzeo, R., Melrose, R.B. «A Signature Formula for Manifolds with Corners of Codimension Two» Topology 36 (1997). | MR | Zbl

[KN] Kobayashi, S., Nomizu, K. : «Foundations of Differential Geometry». Volume I, Interscience Publishers, 1963. | MR | Zbl

[LM] Lawson, H. B., Michelsohn, M. L. : «Spin Geometry.», Princeton University Press, Princeton, New Jersey, 1989. | MR | Zbl

[Mü] Müller, W. : «On the L2-Index of Dirac Operators on Manifolds with Corners of Codimension Two. I» J. Diff. Geo. 44 (1996) 97-177. | Zbl

[Pe] Pedersen, G.K. : «Analysis Now», Springer-Verlag, Graduate Texts in Mathematics 118 (1989) | MR | Zbl

[Sa1] Salomonsen, G. : «The Atiyah-Patodi-Singer Index Theorem for Manifolds with Corners I.» To appear. Available on http://styx.math.uni-bonn.de/~gorm/