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arXiv · 0707.1411

Constructing Simplicial Branched Covers

Nikolaus Witte
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Abstract

Branched covers are applied frequently in topology - most prominently in the construction of closed oriented PL d-manifolds. In particular, strong bounds for the number of sheets and the topology of the branching set are known for dimension d<=4. On the other hand, Izmestiev and Joswig described how to obtain a simplicial covering space (the partial unfolding) of a given simplicial complex, thus obtaining a simplicial branched cover [Adv. Geom. 3(2):191-255, 2003]. We present a large class of branched covers which can be constructed via the partial unfolding. In particular, for d<=4 every closed oriented PL d-manifold is the partial unfolding of some polytopal d-sphere.

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Nikolaus Witte. 2008-01-23. Constructing Simplicial Branched Covers. https://arxiv.org/abs/0707.1411

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