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

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.

Publisher

Springer Verlag

Publication Date

8-1-2015

Publication Title

Boletín de la Sociedad Matemática Mexicana

Department

Mathematics

Document Type

Article

DOI

https://dx.doi.org/10.1007/s40590-015-0067-5

Keywords

Artin presentation, 3-manifold, Secondary homotopy group, Fox Calculus

Language

English

Format

text

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