Topology, geometry, and gauge fields : foundations /

Though mathematicians and physicists have many common concerns, the two disciplines speak different languages, and students of each field do not have an easy time picking up what they need to know from the other. Thus, any book that may function as a Rosetta stone attracts considerable interest. Chapters 1 through 4 of Naber's volume form a reasonably conventional exposition of basic differential topology and geometry through fibre bundles and Lie groups. But since the author has applications to nuclear and particle physics in mind, physics students will find just what they need to know; mathematics students will learn what it all means for physics in the preliminary chapter 0 and in much more detail in the final chapter 5, which treats Yang-Mills theory and matter fields. A very useful book, for upper-division undergraduates and beyond. D. V. Feldman; University of New Hampshire