Variational Problems in Topology

Release on 2019-06-21 | by A.T. Fomenko

... by six elements a1. ,a2,...,a6 A group of orientation-preserving homeotopy of a solid pretzel is generated by the five elements a1, a2,...,a5. 2. ... Fix on a two-dimensional pretzel the set of standard meridians a1,...,ag (Fig. 6).

Author: A.T. Fomenko
Publisher: Routledge
ISBN: 9781351405676
Category: Mathematics
Page: 226
View: 125

Variational Problems in Topology

Many of the modern variational problems of topology arise in different but overlapping fields of scientific study: mechanics, physics and mathematics. In this work, Professor Fomenko offers a concise and clear explanation of some of these problems (both solved and unsolved), using current methods of analytical topology. His book falls into three interrelated sections. The first gives an elementary introduction to some of the most important concepts of topology used in modern physics and mechanics: homology and cohomology, and fibration. The second investigates the significant role of Morse theory in modern aspects of the topology of smooth manifolds, particularly those of three and four dimensions. The third discusses minimal surfaces and harmonic mappings, and presents a number of classic physical experiments that lie at the foundations of modern understanding of multidimensional variational calculus. The author's skilful exposition of these topics and his own graphic illustrations give an unusual motivation to the theory expounded, and his work is recommended reading for specialists and non-specialists alike, involved in the fields of physics and mathematics at both undergraduate and graduate levels.