Geodesic
A Counterexample to the Extension Space Conjecture for Realizable Oriented Matroids
Séminaire lotharingien de combinatoire, 78B (2017)

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The extension space conjecture of oriented matroid theory states that the space of all one-element, non-loop, non-coloop extensions of a realizable oriented matroid of rank d has the homotopy type of a sphere of dimension d-1. We disprove this conjecture by showing the existence of a realizable uniform oriented matroid of high rank and corank 3 with disconnected extension space. 

@article{SLC_2017_78B_a30,
     author = {Gaku Liu},
     title = {A {Counterexample} to the {Extension} {Space} {Conjecture} for {Realizable} {Oriented} {Matroids}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {78B},
     year = {2017},
     url = {http://geodesic.mathdoc.fr/item/SLC_2017_78B_a30/}
}
TY  - JOUR
AU  - Gaku Liu
TI  - A Counterexample to the Extension Space Conjecture for Realizable Oriented Matroids
JO  - Séminaire lotharingien de combinatoire
PY  - 2017
VL  - 78B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2017_78B_a30/
ID  - SLC_2017_78B_a30
ER  - 
%0 Journal Article
%A Gaku Liu
%T A Counterexample to the Extension Space Conjecture for Realizable Oriented Matroids
%J Séminaire lotharingien de combinatoire
%D 2017
%V 78B
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2017_78B_a30/
%F SLC_2017_78B_a30
Gaku Liu. A Counterexample to the Extension Space Conjecture for Realizable Oriented Matroids. Séminaire lotharingien de combinatoire, 78B (2017). http://geodesic.mathdoc.fr/item/SLC_2017_78B_a30/