Splitting criteria for a definite 4-manifold with infinite cyclic fundamental group

Akio Kawauchi

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arXiv · 1804.01380

Splitting criteria for a definite 4-manifold with infinite cyclic fundamental group

Akio Kawauchi

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Abstract

Two criteria for a closed connected definite 4-manifold with infinite cyclic fundamental group to be TOP-split are given. One criterion extends a sufficient condition made in a previous paper. The result is equivalent to a purely algebraic result on the question asking when a positive definite Hermitian form over the ring of integral one-variable Laurent polynomials is represented by an integer matrix. As an application, an infinite family of orthogonally indecomposable unimodular odd definite symmetric $Z$-forms is produced.

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Akio Kawauchi. 2018-04-04. Splitting criteria for a definite 4-manifold with infinite cyclic fundamental group. https://arxiv.org/abs/1804.01380

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