By Matthias Lesch, Bernhelm Booss-Bavnbek, Slawomir Klimek, Weiping Zhang

ISBN-10: 9812568050

ISBN-13: 9789812568052

ISBN-10: 9812773606

ISBN-13: 9789812773609

Sleek thought of elliptic operators, or just elliptic concept, has been formed through the Atiyah-Singer Index Theorem created forty years in the past. Reviewing elliptic conception over a large diversity, 32 best scientists from 14 varied international locations current fresh advancements in topology; warmth kernel ideas; spectral invariants and slicing and pasting; noncommutative geometry; and theoretical particle, string and membrane physics, and Hamiltonian dynamics. the 1st of its variety, this quantity is ultimate to graduate scholars and researchers attracted to cautious expositions of newly-evolved achievements and views in elliptic concept. The contributions are in line with lectures awarded at a workshop acknowledging Krzysztof P Wojciechowski's paintings within the idea of elliptic operators.

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**Extra info for Analysis, Geometry And Topology of Elliptic Operators: Papers in Honor of Krysztof P. Wojciechowski**

**Example text**

We proceed with the construction of c G El\m(E,F) in (3). Let ftp : P —> X be the principal 0(m)-bundle of orthonormal frames of the normal bundle N —> X for the embedding / : X —•> Y, where diraX = n and d i m F = n'. m —> Nx, where m = n' — n and Nx is the fiber of the normal bundle at x G X. In terms of associated bundles, we have N = P x 0 ( m ) Mm = ( P x K m ) / O(m), where O(m) a c t s o n P x R " 1 via (p,v)-A := ( p o i , A~lv). Note that 0(m) also acts on K m + 1 = E m x M via A • (v,a) = (A(v),a), and the m-sphere Sm C E m + 1 is invariant under this action with two fixed points, the poles (0,±1) eSm.

J. Park and K. P. Wojciechowski, Scattering theory and adiabatic decomposition of the (^-determinant of the Dirac Laplacian, Math. Res. Lett. 9 (2002), no. 1, 17-25. 27. J. Park and K. P. Wojciechowski, Adiabatic decomposition of the ^-determinant and Scattering theory, Michigan Math. DG/0111046 . 28. J. Park and K. P. Wojciechowski, Adiabatic decomposition of the zetadeterminant and the Dirichlet to Neumann operator, J. Geom. Phys. 55 (2005), 241-266. 29. J. Park and K. P. Wojciechowski, Agranovich-Dynin formula for the zetadeterminants of the Neumann and Dirichlet problems, Spectral geometry of manifolds with boundary and decomposition of manifolds, 109-121, Contemp.

167-305. 34. K. P. Wojciechowski, The additivity of the rj-invariant. The case of a singular tangential operator, Comm. Math. Phys. 169 (1995), 315-327. 35. K. P. Wojciechowski, The ^-determinant and the additivity of the rj-invariant on the smooth, self-adjoint Grassmannian, Comm. Math. Phys. 201, no. 2 (1999), 423-444. Received by the editors September 15, 2005 ; Revised January 4, 2006 Part II Topological Theories This page is intentionally left blank Analysis, Geometry and Topology of Elliptic Operators, pp.

### Analysis, Geometry And Topology of Elliptic Operators: Papers in Honor of Krysztof P. Wojciechowski by Matthias Lesch, Bernhelm Booss-Bavnbek, Slawomir Klimek, Weiping Zhang

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