Computability Theory and Differential Geometry
From MaRDI portal
Publication:5717234
DOI10.2178/bsl/1102083758zbMath1085.03033OpenAlexW2104375826WikidataQ115230384 ScholiaQ115230384MaRDI QIDQ5717234
Publication date: 12 January 2006
Published in: Bulletin of Symbolic Logic (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2178/bsl/1102083758
Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Applications of computability and recursion theory (03D80) Recursively (computably) enumerable sets and degrees (03D25) Turing machines and related notions (03D10) Manifolds of metrics (especially Riemannian) (58D17)
Related Items
Randomness and reducibility ⋮ Computing All Maps into a Sphere ⋮ Renormalisation and computation II: time cut-off and the Halting Problem ⋮ Randomness and the linear degrees of computability ⋮ Where join preservation fails in the bounded Turing degrees of c.e. sets ⋮ Non-low\(_2\)-ness and computable Lipschitz reducibility ⋮ Computational processes, observers and Turing incompleteness ⋮ Hardness of embedding simplicial complexes in \(\mathbb R^d\) ⋮ Minimal Weak Truth Table Degrees and Computably Enumerable Turing Degrees ⋮ Maximal pairs of computably enumerable sets in the computably Lipschitz degrees ⋮ Bounding Helly Numbers via Betti Numbers ⋮ On the Strongly Bounded Turing Degrees of the Computably Enumerable Sets ⋮ Maximal pairs of c.e. reals in the computably Lipschitz degrees ⋮ Extendability of continuous maps is undecidable ⋮ Effective packing dimension of $\Pi ^0_1$-classes ⋮ Structures of Some Strong Reducibilities ⋮ The settling-time reducibility ordering ⋮ The ibT degrees of computably enumerable sets are not dense ⋮ A uniform version of non-\(\mathrm{low}_{2}\)-ness ⋮ Turing oracle machines, online computing, and three displacements in computability theory ⋮ Computing all maps into a sphere ⋮ Computing simplicial representatives of homotopy group elements ⋮ Computability Results Used in Differential Geometry ⋮ Unnamed Item
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Recursive unsolvability of group theoretic problems
- Generalized Poincaré's conjecture in dimensions greater than four
- The topology of four-dimensional manifolds
- The fractal nature of Riem/Diff. I.
- Algorithmic unsolvability of the triviality problem for multidimensional knots
- Einstein structures: Existence versus uniqueness
- Isoperimetric functions of groups and computational complexity of the word problem
- Disconnectedness of sublevel sets of some Riemannian functionals
- Geometry of the space of triangulations of a compact manifold
- Word problems and recursively enumerable degrees of unsolvability. A sequel on finitely presented groups
- Groups of homotopy spheres. I
- Polyhedral homotopy-spheres
- Hilbert's Tenth Problem is Unsolvable
- Finiteness Theorems for Riemannian Manifolds
- Fundamental group and contractible closed geodesics
- An Unsolvable Problem of Elementary Number Theory
- The word problem
- The word problem