Computability theory and differential geometry

Computability theory and differential geometry

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by Robert I. Soare

Venue:	Bull. Symbolic Logic
Citations:	9 - 0 self

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@ARTICLE{Soare_computabilitytheory,
    author = {Robert I. Soare},
    title = {Computability theory and differential geometry},
    journal = {Bull. Symbolic Logic},
    year = {},
    volume = {10},
    pages = {457--486}
}

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Abstract

Citations

914	On computable numbers, with an application to the ”Entscheidungsproblem - Turing - 1936
545	A Comprehensive Introduction to Differential Geometry - Spivak - 1999
417	Morse theory - Milnor - 1969
225	Topology from the differentiable viewpoint. Based on notes by - Milnor - 1965
214	An unsolvable problem of elementary number theory - Church - 1936
196	Differential Topology - Guillemin, Pollack - 1974
181	The topology of four–dimensional manifolds - Freedman - 1982
152	Algebraic Topology: An Introduction - Massey - 1967
100	Lectures on the h-cobordism theorem - Milnor - 1965
83	Groups of homotopy spheres - Kervaire, Milnor - 1963
68	Hilbert’s tenth problem is unsolvable - Davis - 1973
62	Calculus on Manifolds - Spivak - 1965
57	The Undecidable - Davis - 1965
52	Generalized Poincare's conjecture in dimensions greater than 4 - Smale - 1961
47	Finiteness theorems for Riemannian manifolds - Cheeger - 1970
37	III, On Group-theoretic Decision Problems and their Classification - Miller - 1971
35	The Word problem - Boone - 1959
33	Recursive unsolvability of group theoretic problems - Rabin - 1958
30	E.Rips, Isoperimetric and isodiametric functions of groups - Sapir
26	Insolubility of the problem of homeomorphy - Markov - 1958
24	Soare, Recursively Enumerable Sets and Degrees: A Study of Computable Functions and Computably Generated Sets - I - 1987
18	Certain simple, unsolvable problems of group theory - Boone - 1957
12	On recursively unsolvable problems in topology and their classification, Contributions to Math. Logic (Colloquium - Boone, Haken, et al. - 1966
11	Géométrie Algébrique Réel - Bochnak, Roy - 1987
8	Connections between topological and group theoretical decision problems - Haken - 1973
6	Impossibility of algorithms for recognizing some properties of associative systems - Markov - 1951
6	On the algorithmic unsolvability of the word problem - Novikov
5	Einstein structures: existence versus uniqueness - Nabutovsky - 1995
5	Geometry of the space of triangulations of a compact manifold - Nabutovsky - 1996
4	On algorithmic problems in effectively complete classes of groups - Adjan - 1958
4	Word problems and recursively enumerable degrees of unsolvability, A sequel on finitely presented groups - Boone - 1966
4	The Word Problem - Britton - 1963
4	Lectures on groups of homotopy spheres - Levine - 1983
3	Variational problems for Riemannian functionals and arithmetic groups - Nabutovsky, Weinberger
3	The fractal nature of Riem/Diff - Nabutovsky, Weinberger
2	Computable model theory - Csima - 2003
2	Disconnectedness of sublevel sets of some Riemannian functionals, Geometric and Functional Analysis - Nabutovsky - 1996
2	Fundamental group and contractible closed geodesics - Nabutovsky - 1996
2	Polyhedral homotopy spheres - Stallings - 1960
1	The algorithmic unsolvability of checking certain properties of groups - Adjan - 1955
1	Soare, Applications of computability to differential geometry - Csima, I
1	Non-Recursive Functions, Knots with "Thick Ropes," and Self-Clenching "thick - Nabutovsky - 1995
1	Critical points of Riemannian functionals and arithmetic groups, Math Publ d'IHES - Nabutovsky, Weinberger
1	Analysis situs, J. de l - Poincar'e
1	Moduli: Computation and the large scale geometry of moduli spaces - Weinberger, Computers