Complexity of 3-orbifolds

Details Complexity of 3-orbifolds Complexity of 3-orbifolds

2004-10-20

arxiv.org/abs/math/0410433v1

Topology Appl. 153 (2006), 1658-1681

Mathematics

Geometric Topology

29 pages, 12 figures

Scientific paper

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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