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Modern geometry - methods and applications. Part III. Introduction to homology theory. Transl. from the Russian by Robert G. Burns. (English) Zbl 0703.55001
Graduate Texts in Mathematics, 124. New York etc.: Springer-Verlag. ix, 416 p. DM 138.00 (1990).
This is a translation of the third part of the Russian original (1979; Zbl 0433.53001). It contains the following chapters: Homology and cohomoloy. Computational recipes; Critical points of smooth functions and homology theory; Cobordisms and smooth structures; Bibliography; Appendix 1 (by S. P. Novikov): An analogue of Morse theory for many-valued functions. Certain properties of Poisson brackets; Appendix 2 (by A. T. Fomenko): Plateau’s problem. Spectral bordisms and globally minimal surfaces in Riemannian manifolds; Index; Errata to Parts I and II.

55-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic topology
57Nxx Topological manifolds
57Rxx Differential topology
55M30 Lyusternik-Shnirel’man category of a space, topological complexity à la Farber, topological robotics (topological aspects)
55N10 Singular homology and cohomology theory
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
70Hxx Hamiltonian and Lagrangian mechanics
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)