CAT(0) is an algorithmic property

Elder, M; McCammond, J

CAT(0) is an algorithmic property

Elder, M

McCammond, J

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Publication Type:: Journal Article
Citation:: Geometriae Dedicata, 2004, 107 (1), pp. 25 - 46
Issue Date:: 2004-12-01

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Field	Value	Language
dc.contributor.author	Elder, M https://orcid.org/0000-0002-2438-3945	en_US
dc.contributor.author	McCammond, J	en_US
dc.date.issued	2004-12-01	en_US
dc.identifier.citation	Geometriae Dedicata, 2004, 107 (1), pp. 25 - 46	en_US
dc.identifier.issn	0046-5755	en_US
dc.identifier.uri	http://hdl.handle.net/10453/98847
dc.description.abstract	In this article we give an explicit algorithm which will determine, in a discrete and computable way, whether a finite piecewise Euclidean complex is nonpositively curved. In particular, given such a complex we show how to define a boolean combination of polynomial equations and inequalities in real variables, i.e. a real semi-algebraic set, which is empty if and only if the complex is nonpositively curved. Once this equivalence has been shown, the main result follows from a standard theorem in real algebraic geometry. © 2004 Kluwer Academic Publishers.	en_US
dc.relation.ispartof	Geometriae Dedicata	en_US
dc.relation.isbasedon	10.1023/B:GEOM.0000049096.63639.e3	en_US
dc.subject.classification	General Mathematics	en_US
dc.title	CAT(0) is an algorithmic property	en_US
dc.type	Journal Article
utslib.citation.volume	1	en_US
utslib.citation.volume	107	en_US
utslib.for	0101 Pure Mathematics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
utslib.copyright.status	closed_access
pubs.issue	1	en_US
pubs.publication-status	Published	en_US
pubs.volume	107	en_US

Abstract:

In this article we give an explicit algorithm which will determine, in a discrete and computable way, whether a finite piecewise Euclidean complex is nonpositively curved. In particular, given such a complex we show how to define a boolean combination of polynomial equations and inequalities in real variables, i.e. a real semi-algebraic set, which is empty if and only if the complex is nonpositively curved. Once this equivalence has been shown, the main result follows from a standard theorem in real algebraic geometry. © 2004 Kluwer Academic Publishers.

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http://hdl.handle.net/10453/98847