New PDF release: Combinatorial Geometry in the Plane (translation of

By Hugo Hadwiger, Hans Debrunner (translated by V. Klee)

ISBN-10: 0249790114

ISBN-13: 9780249790115

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Additional info for Combinatorial Geometry in the Plane (translation of Kombinatorische Geometrie in der Ebene, with a new chapter supplied by the translator)

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.

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Combinatorial Geometry in the Plane (translation of Kombinatorische Geometrie in der Ebene, with a new chapter supplied by the translator) by Hugo Hadwiger, Hans Debrunner (translated by V. Klee)


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