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

Husemoller, Dale H.

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)

MSC:

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

Keywords:

gauge group; principal bundle; characteristic classes; smooth manifolds; vector bundles; invariant polynomials; curvature forms; linear connection

Citations:

Zbl 0144.448; Zbl 0307.55015