The diffeomorphism type of small hyperplane arrangements is combinatorially determined
- Gallet, Matteo RICAM, Austrian Academy of Sciences, Linz, Austria
- Saini, Elia Department of Mathematics, University of Fribourg, Switzerland
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2019
Published in:
- Advances in Geometry. - 2019, vol. 19, no. 1, p. 89–100
English
It is known that there exist hyperplane arrangements with the same underlying matroid that admit non-homotopy equivalent complement manifolds. Here we show that, in any rank, complex central hyperplane arrangements with up to 7 hyperplanes and the same underlying matroid are isotopic. In particular, the diffeomorphism type of the complement manifold and the Milnor fiber and fibration of these arrangements are combinatorially determined, that is, they depend only on the underlying matroid. To prove this, we associate to every such matroid a topological space, that we call the reduced realization space; its connectedness, shown by means of symbolic computation, implies the desired result.
- Faculty
- Faculté des sciences et de médecine
- Department
- Département de Mathématiques
- Language
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- English
- Classification
- Mathematics
- License
- License undefined
- Identifiers
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- RERO DOC 324117
- DOI 10.1515/advgeom-2018-0015
- Persistent URL
- https://folia.unifr.ch/unifr/documents/307612
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