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AuthorBoltyanskiฤญ, V. G. author
TitleIntuitive Combinatorial Topology [electronic resource] / by V. G. Boltyanskiฤญ, V. A. Efremovich
ImprintNew York, NY : Springer New York : Imprint: Springer, 2001
Connect tohttp://dx.doi.org/10.1007/978-1-4757-5604-3
Descript XII, 142 p. online resource

SUMMARY

Topology is a relatively young and very important branch of mathematics. It studies properties of objects that are preserved by deformations, twistings, and stretchings, but not tearing. This book deals with the topology of curves and surfaces as well as with the fundamental concepts of homotopy and homology, and does this in a lively and well-motivated way. There is hardly an area of mathematics that does not make use of topological results and concepts. The importance of topological methods for different areas of physics is also beyond doubt. They are used in field theory and general relativity, in the physics of low temperatures, and in modern quantum theory. The book is well suited not only as preparation for students who plan to take a course in algebraic topology but also for advanced undergraduates or beginning graduates interested in finding out what topology is all about. The book has more than 200 problems, many examples, and over 200 illustrations


CONTENT

1 Topology of Curves -- 2 Topology of Surfaces -- 3 Homotopy and Homology -- Appendix A: Topological Objects in Nematic Liquid Crystals -- A.1. Nematics -- A.2. Disclination in the Nematic -- A.3. Disclination and Topology -- A.4. Singular Points -- A.5. What Else Is There?


Mathematics Algebraic geometry Algebraic topology Fluids Mathematics Algebraic Topology Algebraic Geometry Fluid- and Aerodynamics



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