The explicit algebraic autonomy of Artin presentation theory and the Fox Calculus. I

Title:
The explicit algebraic autonomy of Artin presentation theory and the Fox Calculus. I
Authors:
Calcut, Jack S.; Winkelnkemper, Horst E.
Abstract:
Given an Artin presentation r, we use the Fox Calculus to obtain a short, purely algebraic computation, just in function of r, of the second homotopy group of the associated manifold M3(r)M3(r). This allows us to give a Langlands-like formulation (not yet a proof) of the three-dimensional Borel conjecture for closed, orientable 3-manifolds, the latter being a theorem of geometrization theory and implying the Poincaré conjecture.
Citation:
Calcut, J.S., and H.E. Winkelnkemper. 2015. "The explicit algebraic autonomy of Artin presentation theory and the Fox Calculus. I." Boletín de la Sociedad Matemática Mexicana: 1-11.
Publisher:
Springer Verlag
DATE ISSUED:
2015-08
Department:
Mathematics
Type:
Article
PUBLISHED VERSION:
10.1007/s40590-015-0067-5
PERMANENT LINK:
http://hdl.handle.net/11282/599294

Full metadata record

DC FieldValue Language
dc.contributor.authorCalcut, Jack S.en
dc.contributor.authorWinkelnkemper, Horst E.en
dc.date.accessioned2016-02-26T14:29:36Zen
dc.date.available2016-02-26T14:29:36Zen
dc.date.issued2015-08en
dc.identifier.citationCalcut, J.S., and H.E. Winkelnkemper. 2015. "The explicit algebraic autonomy of Artin presentation theory and the Fox Calculus. I." Boletín de la Sociedad Matemática Mexicana: 1-11.en
dc.identifier.issn1405-213Xen
dc.identifier.urihttp://hdl.handle.net/11282/599294en
dc.description.abstractGiven an Artin presentation r, we use the Fox Calculus to obtain a short, purely algebraic computation, just in function of r, of the second homotopy group of the associated manifold M3(r)M3(r). This allows us to give a Langlands-like formulation (not yet a proof) of the three-dimensional Borel conjecture for closed, orientable 3-manifolds, the latter being a theorem of geometrization theory and implying the Poincaré conjecture.en
dc.language.isoen_USen
dc.publisherSpringer Verlagen
dc.identifier.doi10.1007/s40590-015-0067-5en
dc.subject.departmentMathematicsen_US
dc.titleThe explicit algebraic autonomy of Artin presentation theory and the Fox Calculus. Ien_US
dc.typeArticleen
dc.identifier.journalBoletín de la Sociedad Matemática Mexicanaen
dc.subject.keywordArtin presentationen_US
dc.subject.keyword3-manifolden_US
dc.subject.keywordSecondary homotopy groupen_US
dc.subject.keywordFox Calculusen_US
dc.identifier.startpage1en_US
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