Graham P. Collins

FORMS OF SPACE

Grigoriy Yakovlevich Perelman proved the Poincare theorem for a variety of three-dimensional and three-dimensional spheres. This theorem remained in the famous list of the most intractable problems in science at the beginning of the century : the "Millennium Prize's Problems" ("Millennium Challenges"). It took almost four years (from the date of the publications by G. Perelman) to the world's biggest "authorities" in mathematics to conceal that the proof was correct …

The TFF developed by I.L. Gerlovin in collaboration with other scientists, is based on a few basic principles as well as some mathematical constructions. One of the main of them says : "space is to be considered as a fiber multi-dimensional space". Each layer (subspace) is linked in a certain way to the other, and their combination corresponds to the principles set forth in the Paradigm of Gerlovin. And the enclosing "zero" space is a geometric structure of our universe - a space corresponding indeed to a 3-dimensional sphere (S3)…

Sergei Poleshchuk

POINCARE' THEOREM IN SIMPLE WORDS

Jules Henri Poincaré (1854-1912) headed the Paris Academy of Sciences and was elected to the scientific academies of 30 countries. His talent was comparable to the one of Leonardo de Vinci, and his interests included physics, mechanics, astronomy, and philosophy. Mathematics all over the world still think that only two people in the history truly knew this science: the German David Gilbert (1862-1943) and Henri Poincaré…

In 1904, the scientist published a paper which contained, inter alia, an assumption, called the Poincaré theorem. The search for the proof of this statement took nearly a century.

V.A. Uspensky

THE THEOREM OF POINCARÉ - PERELMAN SET FORTH BY V.A. USPENSKY

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B.A. Dubrovin, S.P. Novikov, A.T. Fomenko

MODERN GEOMETRY. METHODS OF THE HOMOLOGY THEORY,

"Nauka". Main editorial physical and mathematical literature, 1984

Over the past 10 years, the topology methods played a great role on the development of some of the most advanced areas of mathematics, mechanics, as well as modern theoretical and mathematical physics.

The book relies on a textbook by the same authors ("Modern Geometry", published in 1979). It lists the available methods of the homology theory, freed from the tedious language of abstract algebra homology. A more complex part of the book provides an introduction to modern methods of computing homotopic groups and classification of varieties.

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T. Lebedev

WORKS BY THE LENINGRAD SOCIETY OF NATURALISTS,

Publication of the Leningrad University, 1968

The author draws attention to the generally known fact that theoretical physics is now experiencing great difficulties in generalization of many of experimental facts.

Under these conditions, the question of improving the foundations of the modern theory inevitably raises. It is believed that this can be done with the help of some very unusual, non orthodox ideas. However, the solution must be sought at first by identifying the physical relations between objective facts and, consequently, by the disclosure of a deep continuity between the existing theories.

The main part of this work is devoted to a specific identification of some general principles that could lead to a proper coordination of theories. While opposites and differences exist in nature, they have only a relative value…