Whitehead graph feature-region conjecture

Let FF be a free group, and associate to each element of FF the feature vector of weights of its Whitehead Graph in the corresponding feature space. A region is a bounded subset of that space whose boundary can be described by a hypersurface. Whitehead graph feature-region conjecture. These feature vectors are separated into bounded regions, each of which can be bounded by a hypersurface and corresponds to a particular Nielsen automorphism, in the sense that all elements in the corresponding class can be reduced by that automorphism. The conjecture is explicitly described as vague and is proposed as a model for the behavior of non-minimal elements; the source provides experimental motivation but no proof or resolution.

Sources & referencesView supporting material

Primary source

R. M. Haralick, A. D. Miasnikov and A. G. Myasnikov, “Heuristics for The Whitehead Minimization Problem”, arXiv:math/0604204 (2006).

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