271.19.17  Algebraic topology

271.19.17.17  General theorems on fundamental categories and functors
271.19.17.17.17  General topological categories
271.19.17.17.17.15  Homology and cohomology groups (definitions and basic properties).  
		Axiomatics
271.19.17.17.17.17  Investigation of topological spaces and continuous mappings by 
		homological methods
271.19.17.17.17.17.15  Homology theory of dimension
271.19.17.17.17.17.21  Spectral sequence of a continuous mapping
271.19.17.17.17.17.27  Homology theory of fixed points and coincidence points
271.19.17.17.17.17.33  Homology manifolds
271.19.17.17.17.19  Homology and cohomology with nonabelian coefficients
271.19.17.17.17.25  Homotopy and cohomotopy groups:  definitions and basic 	
		properties.  Axiomatics, etc.
271.19.17.17.17.25.25  Localization of topological spaces
271.19.17.17.17.27  Shape theory
271.19.17.17.17.31  Functors with values in general topological categories (operations over 
		topological spaces)
271.19.17.17.17.31.17  General theory of such functors.  Duality
271.19.17.17.17.31.25  Concrete functors
271.19.17.17.19  Polyhedral categories, i.e., categories whose volumes are polyhedra
271.19.17.17.19.17  Cellular partitions
271.19.17.17.19.19  Simplicial partitions (triangulations) and simplicial schemes
271.19.17.17.21  Categories that approximate general topological and polyhedral categories
271.19.17.17.21.17  Categories whose morphisms are stationary mappings or their 
		homotopy classes (categories of spectra, S-categories)
271.19.17.17.21.17.17  S-duality
271.19.17.17.21.17.21  Adams spectral sequence
271.19.17.17.21.17.25  Extraordinary homology and cohomology theories
271.19.17.17.21.17.27  Bordism and cobordism
271.19.17.17.21.21  Categories of semi-exact functors
271.19.17.17.25  Simplicial sets
271.19.17.19  Homotopy theory:  fundamental problems
271.19.17.19.17  Decompositions of spaces and mappings
271.19.17.19.17.17  Homotopic resolvents ( Moore-Postnikov systems)  and dual 
		constructions
271.19.17.19.17.25  Homotopic convolutions of of spaces (decreasing homotopic groups)
271.19.17.19.17.33  Categories of spaces  (in the sense of Lyusternik-Shnirel'man)
271.19.17.19.19  Obstruction theory.  General classification and continuation theorems for 
		continuous mappings and intersecting surfaces
271.19.17.19.25  Cohomology operations
271.19.17.19.25.33  Analogues of cohomology operations
271.19.17.25  Spaces with various complemented properties of a general nature or that are 
		obtained by these or other general constructions
271.19.17.25.17  Fiber spaces and crossed products
271.19.17.25.17.17  Definition and basic properties, operations over fiber spaces and 
		crossed products
271.19.17.25.17.19  Homotopy theory of bundles.  Universal bundles and classifying 
		spaces
271.19.17.25.17.25  Homology theory of fiber spaces
271.19.17.25.17.25.19  Crossed tensor products
271.19.17.25.17.25.27  Spectral sequences
271.19.17.25.17.31  General theorems on bundles with a vector fiber (K- and J-functors)
271.19.17.25.19  Spaces with operators
271.19.17.25.25  Spaces with multiplication  (H-spaces) and loop spaces
271.19.17.25.27  Space with comultiplication,  and surgeries
271.19.17.25.33  Spaces in which there are only a finite number of nonzero homotopy 
		groups
271.19.17.25.33.21  Eilenberg-MacLane spaces
271.19.17.25.33.27  Spaces in which there are only two nonzero homotopy groups
271.19.17.27  Concrete spaces.  Calculation of homotopy invariants
271.19.17.27.17  Computation of homotopy groups
271.19.17.27.17.19  Homotopy groups of spheres
271.19.17.27.19  Computation of homology and cohomology groups
271.19.17.27.25  Computation of K- and J-functors
271.19.17.27.27  Computation of bordism and cobordism groups
271.19.17.33  Isotopy theory

271.19.19.  Topology of manifolds

271.19.19.17  Topology of manifolds of lower dimensions
271.19.19.17.17  Topological surfaces
271.19.19.17.19  Three-dimensional topological manifolds
271.19.19.17.19.17  Classification of three-dimensional manifolds
271.19.19.17.19.17.19  Poincare conjecture and related problems
271.19.19.17.21  Four-dimensional topological manifolds
271.19.19.17.21.17  Classification of four-dimensional manifolds
271.19.19.17.21.17.19  Poincare conjecture for four-dimensional manifolds
271.19.19.17.27  Embeddings and immersions in lower dimensions
271.19.19.17.33  Knots.  Wreaths.  Braids
271.19.19.19  Topological manifolds
271.19.19.19.19  Microsheaves of topological manifolds
271.19.19.19.27  Topological embeddings and immersions
271.19.19.21  Topology of smooth and piecewise-linear manifolds
271.19.19.21.15  General questions
271.19.19.21.15.15  Homology theory of smooth manifolds
271.19.19.21.15.19  Differential forms on smooth manifolds
271.19.19.21.15.25  Singularities of smooth manifolds
271.19.19.21.15.25.17  Critical points of smooth mappings
271.19.19.21.15.31  Infinite-dimensional manifolds
271.19.19.21.15.31.21  Morse theory
271.19.19.21.17  Classification of smooth and piecewise-linear manifolds
271.19.19.21.17.17  Correspondences between homotopic, topological, combinatorial and 
		smooth properties
271.19.19.21.17.17.25  Realization of cycles
271.19.19.21.17.21  Bordisms and cobordisms
271.19.19.21.17.25  Classification of manifolds up to diffeomorphism or piecewise-linear 
		equivalence
271.19.19.21.17.25.15  Combinatorial equivalence of polyhedra.  Simple homotopy type 
271.19.19.21.19  Bundles of smooth manifolds and bundles whose bases are smooth 
		manifolds
271.19.19.21.19.17  Characteristic classes of manifolds
271.19.19.21.19.17.17  Vector fields on manifolds
271.19.19.21.19.25  Microbundles
271.19.19.21.27  Smooth and piecewise-linear embeddings and embeddings of manifolds
271.19.19.21.33  Groups that act on smooth and piecewise-linear manifolds
271.19.19.21.33.25  Groups of diffeomorphisms and piecewise-linear equivalences
271.19.19.25  Topology of smooth manifolds endowed with complemented structure
271.19.19.25.17  Topology of complex and almost complex manifolds
271.19.19.25.21  Topology of Kahlerian and algebraic manifolds
271.19.19.25.31  Topology of manifolds with infinitesimal connection.  Topology of 
		Riemannian manifolds
271.19.19.33  Differential and integral operators on manifolds
271.19.19.33.19  Foliations.  Integration of vector and tensor fields
271.19.19.33.25  Elliptic operators on manifolds
271.19.21  Analytic spaces
271.19.21.15  General theory of complex and real analytic spaces
271.19.21.15.15  Local theory
271.19.21.15.17  Classes of analytic spaces identified by local conditions
271.19.21.15.19  General theory of coherent analytic sheaves and their cohomology
271.19.21.15.19.19  A connection between the cohomologies of complex spaces and 
		differential forms
271.19.21.15.19.19.21  Residues of differential forms
271.19.21.15.19.25   Computation of the cohomology of specific complex spaces 
271.19.21.15.19.27  The Riemann-Roch theorem for complex manifolds, and related 
		problems
271.19.21.15.25  Analytic sets, subspaces and submanifolds
271.19.21.15.27  Integration on analytic sets and analytic spaces
271.19.21.15.31  Intrinsic metrics on complex spaces
271.19.21.17  Analytic mappings and constructions of complex spaces
271.19.21.17.17  Holomorphic mappings of complex spaces
271.19.21.17.17.17  Holomorphic functions.  Domains and holomorphy hulls in analytic 
		spaces
271.19.21.17.17.19  Cohomology investigation of holomorphic mappings
271.19.21.17.17.25  Approximation theorems for holomorphic functions and mappings in 
		analytic spaces.  Runge pairs
271.19.21.1719  Plurisubharmonic functions, pseudo-convex and pseudo-concave 
		domains in analytic spaces and their generalizations
271.19.21.17.19.19  The Levi problem for analytic spaces
271.19.21.17.21  Meromorphic mappings
271.19.21.17.21.17  Fields of meromorphic functions
271.19.21.17.21.21  Cousin and Poincare problems for analytic spaces
271.19.21.17.27  Quotient spaces of complex spaces 
271.19.21.17.31  Analytic coverings
271.19.21.17.33  Modification of complex spaces
271.19.21.17.33.19  Resolution of singularities of complex spaces and mappings
271.19.21.19  Complex spaces of one, two and three dimensions
271.19.21.19.17  One-dimensional complex manifolds
271.19.21.19.21  Complex surfaces
271.19.21.19.21.15  Singular points of complex surfaces
271.19.21.19.27  Three-dimensional complex spaces
271.19.21.21  Classes of complex spaces distinguished by global conditions
271.19.21.21.17  Holomorphically convex spaces
271.19.21.21.19  Holomorphically complete spaces
271.19.21.21.21.  q-pseudo-convex, q-pseudo-concave and q-complete spaces
271.19.21.21.25  Complex spaces that are close to algebraic manifolds
271.19.21.21.31  Global properties of real-analytic spaces
271.19.21.25  Generalizations of analytic spaces
271.19.21.25.17  Banach analytic spaces
271.19.21.25.21  Partially analytic and other spaces
271.19.21.25.31  Analytic investigation of almost complex manifolds
271.19.21.27  Holomorphic fiber spaces
271.19.21.27.17  Classification of holomorphic fiber spaces 
271.19.21.27.19  Holomorphic vector fiber spaces and sheaves and related cohomologies
271.19.21.27.21  Holomorphic and meromorphic sections in fiber spaces
271.19.21.27.27  A connection between the theory of fiber spaces and some problems in 
		analysis
271.19.21.27.33  Holomorphic connections in fiber spaces
271.19.21.31  Complex spaces with an automorphism group
271.19.21.31.17  Complex Lie transformation groups
271.19.21.31.21  Automorphism groups of complex and almost complex spaces
271.19.21.21.25  Complex homogeneous spaces
271.19.21.21.25.17  Compact complex homogeneous spaces
271.19.21.21.25.19  Kahlerian homogeneous spaces.  Homogeneous domains
271.19.21.21.25.21  Analytic functions on homogeneous spaces
271.19.21.21.25.27  Homogeneous vector fiber spaces and related cohomologies
271.19.21.33  Automorphic functions
271.19.21.33.15  Automorphic and modular forms
271.19.21.33.17  Abelian functions
271.19.21.33.19  Modular functions
271.19.21.33.25  Automorphic forms and related cohomologies
271.19.21.33.27  Automorphic functions in symmetric domains
271.19.21.39  Deformations of structures.  Pseudogroups
271.19.21.39.15  Cohomology problems in the theory of pseudogroups
271.19.21.39.17  Deformations of complex structures
271.19.21.39.17.17  Deformations of submanifolds and holomorphic mappings
271.19.21.39.17.19  Extension of analytic objects
271.19.21.39.17.25  Theory of moduli of Riemann surfaces
271.19.21.39.19  Deformations of other pseudogroup structures
271.19.21.39.21  Deformations of G-structures and connections
271.19.21.39.25  Deformations of fiber spaces
271.19.21.39.33  Analytic theory of deformations of algebraic structures

271.21  Geometry

271.21.15  Geometry in spaces with fundamental groups
271.21.15.15  Elementary geometry, trigonometry, polygonometry
271.21.15.15.17  Planimetry
271.21.15.15.17.19  Triangle geometry
271.21.15.15.17.21  Geometry of polygons (including rectangles, etc.)
271.21.15.15.17.27  Elementary circle geometry
271.21.15.15.19  Stereometry

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