# Is topology math or physics

## Differential Geometry, Topology and Physics

Differential geometry and topology are important tools for theoretical physics. In particular, they are used in the fields of astrophysics, particle and solid-state physics. This popular book, which has now been translated into German for the first time, is an ideal introduction for master’s students and researchers in the field of theoretical and mathematical physics.

- In the first chapter the book offers an overview of the path integral method and gauge theories.

- Chapter 2 deals with the mathematical basics of mappings, vector spaces and topology.

- The following chapters deal with more advanced concepts of geometry and topology and also discuss their applications in the field of liquid crystals, superfluid helium, GTR, and bosonic string theory.

- This is followed by a merging of geometry and topology: it is about fiber bundles, characteristic classes and index theorems (e.g. in application to supersymmetric quantum mechanics).

- The last two chapters are devoted to the most exciting application of geometry and topology in modern physics, namely gauge field theories and the analysis of Polakov's bosonic string theory from a metric perspective.

**Mikio Nakahara** studied physics as well as classical and quantum gravity theory at Kyoto University and at King’s in London. Today he is professor of physics at Kinki University in Osaka (Japan), where he is a. researches on topological quantum computers. This book is the result of a lecture he gave during research stays at the University of Sussex and the Helsinki University of Sussex.

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