Variational Problems in Topology

Offers an explanation of both solved and unsolved problems in current methods of analytical topology. Subjects discussed include homology, cohomology, fibration, the role of Morse theory in modern aspects of the topology of smooth manifolds, minimal surfaces and harmonic mappings.

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Many of the modern variational problems in topology arise in different but overlapping fields of scientific study: mechanics, physics and mathematics. In this work, Professor Fomenko offers a concise and clean explanation of some of these problems (both solved and unsolved), using current methods and analytical topology. The author's skillful exposition gives an unusual motivation to the theory expounded, and his work is recommended reading for specialists and nonspecialists alike, involved in the fields of physics and mathematics at both undergraduate and graduate levels.