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Kervaire Conjecture


The Kervaire conjecture in group theory asserts that adjoining one generator and imposing one relation on a nontrivial group cannot give the trivial group. For a nontrivial group G and w in G*<t>, it predicts

 (G*<t>)/<<w>>!={1},

where <t>=Z and the denominator is the normal closure of w. This is distinct from the Kervaire characterization theorem for knot groups.


See also

Free Product, Group Equation, Howie Conjecture, Kervaire's Characterization Theorem, Normal Closure

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References

Chen, L. "The Kervaire Conjecture and the Minimal Complexity of Surfaces." Trans. Amer. Math. Soc. 379, 587-626, 2026. https://doi.org/10.1090/tran/9490.

Cite this as:

Weisstein, Eric W. "Kervaire Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/KervaireConjecture.html

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