6533b861fe1ef96bd12c4509

RESEARCH PRODUCT

Open and Discrete Maps with Piecewise Linear Branch Set Images are Piecewise Linear Maps

Eden PrywesRami LuistoRami Luisto

subject

Mathematics - Complex VariablesGeneral MathematicsImage (category theory)010102 general mathematicsGeometric Topology (math.GT)01 natural sciencesHomeomorphismPiecewise linear functionSet (abstract data type)CombinatoricsfunktioteoriaMathematics - Geometric TopologyCover (topology)0103 physical sciencesFOS: MathematicsHigh Energy Physics::Experiment010307 mathematical physicsComplex Variables (math.CV)0101 mathematicstopologiaMathematics

description

The image of the branch set of a piecewise linear (PL)‐branched cover between PL 𝑛n‐manifolds is a simplicial (𝑛−2)(n−2)‐complex. We demonstrate that the reverse implication also holds: an open and discrete map 𝑓:𝕊𝑛→𝕊𝑛f:Sn→Sn with the image of the branch set contained in a simplicial (𝑛−2)(n−2)‐complex is equivalent up to homeomorphism to a PL‐branched cover. peerReviewed

yearjournalcountryeditionlanguage
2018-09-28
10.1112/jlms.12404http://arxiv.org/abs/1809.10874