Journal article

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
    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
  • English
Classification
Mathematics
License
License undefined
Identifiers
Persistent URL
https://folia.unifr.ch/unifr/documents/307612
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