Topology for Physicists by Albert S. Schwarz (PDF)

Description

0 Background.- 1 Fundamental Concepts.- 2 The Degree of a Map.- 3 The Fundamental Group and Covering Spaces.- 4 Manifolds.- 5 Differential Forms and Homology in Euclidean Space.- 6 Homology and Cohomology.- 7 Homotopy Classification of Maps of the Sphere.- 8 Homotopy Groups.- 9 Fibered Spaces.- 10 Fibrations and Homotopy Groups.- 11 Homotopy Theory of Fibrations.- 12 Lie Groups.- 13 Lie Algebras.- 14 Topology of Lie Groups and Homogeneous Manifolds.- 15 Geometry of Gauge Fields.- Index of Notation.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐As befits a book which concerns itself with topological matters, from the purely qualitative viewpoint this is an excellent text. On the narrative front it is also a superb read. Not exactly a bodice-ripper, of course, but about as good as one might reasonably expect from a book on such an abstract topic. Consequently, Schwarz’s text has earned itself something of a reputation as a standard beginner’s guide in the physics community. Overall, it covers with some elegance and style the basic core of material concerning topological matters that is increasingly seen as required background knowledge for a contemporary PhD student of theoretical physics, and does this in such a way as to strike a very reasonable balance between formalism and transparency, with plenty of examples to guide the way, the latter of course being frowned upon by the higher-minded authors of the “pure” mathematical community who strive to write books of such abstract perfection, as to be beyond all mortal comprehension, yielding their secrets -presumably- to only the most select of mathematical deities.From a quantitative standpoint, however, as perhaps also fits a title on topology, this book is sadly a disaster. As unfortunately, almost no one in its intended readership will be able to afford a copy. Indeed, the book has been priced at a level which is about a factor of three or four beyond a sane student’s budget, and at a similar factor more than other excellent books which cover much of the same material at the same level, such as Nakahara’s

⭐, Frankel’s

⭐and the less well-known, but also very good,

⭐, by Hou and Hou. Another excellent book worth mentioning, which is perhaps closest to Schwarz’s in content and style, is Nash and Sen’s

⭐. This, once very reasonably priced gem, is however currently sadly out of print. Its really not clear why Schawrz’s book is so expenssive. It is most definitely not an advanced or specialised text, but rather an introductory pedagogical one. Moreover, it is actually considerably more expensive than many more advanced mathematical texts on the same subject and also many of the the original specialised texts which it essentially summarises. Indeed, its hard to think of another physics text book that is so expensive. Did I mention how expensive it was? Still, putting earthly economic matters aside, Topology for Physicists is a great book, definitely worth obtaining from a library, and above all, definitely worth a read!

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