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arXiv · 0808.1058

The Laurent norm

David G. Long
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Abstract

We generalize a semi-norm for the Alexander polynomial of a connected, compact, oriented 3-manifold on its first cohomology group to a semi-norm for an arbitrary Laurent polynomial f on the dual vector space to the space of exponents of f. We determine a decomposition formula for this Laurent norm; an expression for the Laurent norm for f in terms of the Laurent norms for each of the irreducible factors of f. For an n-variable polynomial f, we introduce a space of m \leq n essential variables which determine the reduced Laurent norm unit ball; a convex polyhedron of the same dimension m as the Newton polyhedron of f. In the space spanned by the essential variables, the Laurent semi-norm for polynomials with at least two terms is shown to be a norm.

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David G. Long. 2008-08-07. The Laurent norm. https://arxiv.org/abs/0808.1058

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