Complexity of 3-orbifolds

Carlo Petronio

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Complexity of 3-orbifolds

Carlo Petronio

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Abstract

We extend Matveev's theory of complexity for 3-manifolds, based on simple spines, to (closed, orientable, locally orientable) 3-orbifolds. We prove naturality and finiteness for irreducible 3-orbifolds, and, with certain restrictions and subtleties, additivity under orbifold connected sum. We also develop the theory of handle decompositions for 3-orbifolds and the corresponding theory of normal 2-suborbifolds.

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Carlo Petronio. 2004-10-20. Complexity of 3-orbifolds. https://arxiv.org/abs/math/0410433

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