Dubrovin, B. A.; Fomenko, A. T.; Novikov, S. P. 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. Cited in 3 ReviewsCited in 31 Documents MSC: 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.) Keywords:simplicial homology; Čech cohomology; homology theory; de Rham cohomology; singular homology; cohomology with local coefficients; cohomology rings of H-spaces; Lie groups; homology of bundles; characteristic classes; cohomology operations; rational homotopy groups; Poincaré duality; Lyusternik-Shnirel’man category; calculus of variations; geodesics; Bott periodicity; n-body problem in the plane; smooth cobordism; signature; representability of homology classes; rational Pontryagin classes; h-cobordism groups; smooth structures on manifolds; Critical points; Morse theory; Poisson brackets; Plateau’s problem; Spectral bordisms; globally minimal surfaces PDF BibTeX XML Cite \textit{B. A. Dubrovin} et al., Modern geometry - methods and applications. Part III. Introduction to homology theory. Transl. from the Russian by Robert G. Burns. New York etc.: Springer-Verlag (1990; Zbl 0703.55001)