By Michael Spivak

ISBN-10: 0914098748

ISBN-13: 9780914098744

Publication by means of Michael Spivak

**Read or Download A Comprehensive Introduction to Differential Geometry, Vol. 5, Third Edition PDF**

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**Additional resources for A Comprehensive Introduction to Differential Geometry, Vol. 5, Third Edition**

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Shaneson, Genera of algebraic varieties and counting lattice points, Bull. AMS 30 (1994), 62--69. E. L. R. Acad. Sci. Paris Sr. I Math. 321 (1995), 885-890. [DR] R. Diaz and S. Robins, The Ehrhart Polynomial of a Lattice Polytope, Ann. Math. (2) 145(3) (1997), 503 518, and Erratum: "The Ehrhart polynomial of a lattice polytope", Ann. Math. (2) 146(1) (1997), 237. IEhr] E. R. Acad. Sci. Paris 254 (1962), 616--618. [FG] L. Friedlander and V. -S. Chern. [Gugau] V. Guillemin, Gauged Lagrangian distributions, Adv.

Math. Phys. 37 (1996), 3422 3441. [11) T. Ioannidou and W. Zakrzewski, Solutions of the modified chiral model in (2 + 1) dimensions, J. Math. Phys. 39(5) (1998), 2693-2701. [12) T. Ioannidou and W. Zakrzewski, Lagrangian formulation of the general modified chiral model, Phys. Lett. A 249 (1998), 303 306. V. E. Zakharov, Three-dimensional model of relativistic-invariant theory, integrable by the inverse scattering transform, Lett. Math. Phys. 5 (1981), 247 253. [14] A. Pressley and G. Segal, Loop groups, Oxford University Press, 1986.

A derivative of a homogeneous summand in (6) is itself a homogenous function. So as N - 00, the integral of this derivative over a face of the polytope is a homogenous function in N whose degree depends on the degree of this derivative and the dimension of the face. So the contributions of the polyhomogenous terms with sufficiently negative degree in (6) will be homogeneous terms of high negative degree in N in (15). By the same token, each homogenous summand in (6) will yield THE EHRHART FUNCTION FOR SYMBOLS 37 a finite number of terms to each order in (15).

### A Comprehensive Introduction to Differential Geometry, Vol. 5, Third Edition by Michael Spivak

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