Fibre bundles. 3rd ed. (English) Zbl 0794.55001

Graduate Texts in Mathematics. 20. Berlin: Springer-Verlag. xix, 353 p. (1993).
In this third edition of his well known book [for the first edition (1966) see Zbl 0144.448, for the second edition (1975) see Zbl 0307.55015], the author has introduced two new chapters: 7 and 19. In Chapter 7 he considers the gauge group of a principal bundle, which has numerous applications in differential geometry and mathematical physics. In Chapter 19, starting from A. Weil’s viewpoint, the author calculates the characteristic classes of smooth manifolds and vector bundles, using the invariant polynomials associated to the curvature forms for a linear connection. This bibliography has been enlarged and updated.
Reviewer: V.Cruceanu (Iaşi)


55-02 Research exposition (monographs, survey articles) pertaining to algebraic topology
55R10 Fiber bundles in algebraic topology
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14F40 de Rham cohomology and algebraic geometry