scholarly journals The Slack Realization Space of a Polytope

2019 ◽  
Vol 33 (3) ◽  
pp. 1637-1653 ◽  
Author(s):  
João Gouveia ◽  
Antonio Macchia ◽  
Rekha R. Thomas ◽  
Amy Wiebe
Keyword(s):  
Realization Space

scholarly journals The diffeomorphism type of small hyperplane arrangements is combinatorially determined

2019 ◽  
Vol 19 (1) ◽  
pp. 89-100
Author(s):  
Matteo Gallet ◽  
Elia Saini
Keyword(s):  
Topological Space ◽  
Symbolic Computation ◽  
Hyperplane Arrangements ◽  
Homotopy Equivalent ◽  
Milnor Fiber ◽  
Realization Space ◽  
Diffeomorphism Type

Abstract 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.

scholarly journals The slack realization space of a matroid

2019 ◽  
Vol 2 (4) ◽  
pp. 663-681 ◽  
Author(s):  
Madeline Brandt ◽  
Amy Wiebe
Keyword(s):  
Realization Space
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