Computability Results Used in Differential Geometry

Journal of Symbolic Logic 71 (4):1394 - 1410 (2006)
Abstract
Topologists Nabutovsky and Weinberger discovered how to embed computably enumerable (c.e.) sets into the geometry of Riemannian metrics modulo diffeomorphisms. They used the complexity of the settling times of the c.e. sets to exhibit a much greater complexity of the depth and density of local minima for the diameter function than previously imagined. Their results depended on the existence of certain sequences of c.e. sets, constructed at their request by Csima and Soare, whose settling times had the necessary dominating properties. Although these computability results had been announced earlier, their proofs have been deferred until this paper. Computably enumerable sets have long been used to prove undecidability of mathematical problems such as the word problem for groups and Hilbert's Tenth Problem. However, this example by Nabutovsky and Weinberger is perhaps the first example of the use of c.e. sets to demonstrate specific mathematical or geometric complexity of a mathematical structure such as the depth and distribution of local minima
Keywords No keywords specified (fix it)
Categories (categorize this paper)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 10,941
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

No references found.

Citations of this work BETA
Similar books and articles
John P. Burgess (1988). Sets and Point-Sets: Five Grades of Set-Theoretic Involvement in Geometry. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1988:456 - 463.
E. Börger (1989). Computability, Complexity, Logic. New York, N.Y., U.S.A.Elsevier Science Pub. Co..
Wolfgang Maass (1982). Recursively Enumerable Generic Sets. Journal of Symbolic Logic 47 (4):809-823.
Analytics

Monthly downloads

Added to index

2010-08-24

Total downloads

2 ( #347,663 of 1,100,740 )

Recent downloads (6 months)

1 ( #289,271 of 1,100,740 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Start a new thread
Order:
There  are no threads in this forum
Nothing in this forum yet.