Zentralblatt MATH Database 1931 – 2006 Zbl 1040.57001 Guillemin

Zentralblatt MATH Database 1931 – 2006 Zbl 1040.57001 Guillemin

Zentralblatt MATH Database 1931 – 2006
c 2006 European Mathematical Society, FIZ Karlsruhe & Springer-Verlag
Zbl 1040.57001
Guillemin, Victor; Pollack, Alan
Differential topology. (Topologı́a diferencial.) (Spanish)
Aportaciones Matematicas, Textos 20(Nivel Medio). México: Sociedad Matemática
Mexicana. xiii, 294 p. (2003).
This is the Spanish translation of the now classical Guillemin-Pollack book on Differential Topology which appeared in 1974 [V. Guillemin and A. Pollack, Differential
topology (1974; Zbl 0361.57001)]. The contents of the book are as follows: 1. Manifolds
and smooth maps; 2. Transversality and intersection; 3. Oriented intersection theory;
4. Integration on manifolds. There are two Appendices: 1. Measure zero and Sard’s
theorem; 2. Classification of compact one-manifolds.
The book is still of great interest and the translation is correct. Unfortunately, some
known misprints of the original edition have not been corrected, and the bibliography
has not been updated. For the Spanish reader a more recent book covering similar
topics is [E. Outerelo and J. M. Ruiz, Differential topology. Manifolds with boundary,
transversality, approximation (1998; Zbl 0889.57001)].
Enrique Macias-Virgós (Santiago de Compostela)
Keywords : manifolds; Sard’s theorem; transversality; stability; Morse functions; manifolds with boundary; intersection theory; winding number; Borsuk-Ulam theorem; orientation; Lefschetz fixed-point theory; Poincaré-Hopf theorem; degree; Euler characteristic; differential forms; integration on manifolds; De Rham cohomology; Stokes theorem;
Gauss-Bonnet theorem; compact 1-manifolds
Classification :
∗ 57-01 Textbooks (manifolds)