On the realization space of the cube
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On the realization space of the cube. / Adiprasito, Karim Alexander; Kalmanovich, Daniel; Nevo, Eran .
In: Séminaire Lotharingien de Combinatoire, Vol. 84B, 80, 2020.Research output: Contribution to journal › Conference article › Research › peer-review
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TY - GEN
T1 - On the realization space of the cube
AU - Adiprasito, Karim Alexander
AU - Kalmanovich, Daniel
AU - Nevo, Eran
PY - 2020
Y1 - 2020
N2 - We prove that the realization space of the d-dimensional cube is contractible. For this we first show that any two realizations are connected by a finite sequence of projective transformations and normal transformations. As an application we use this fact to define an analog of the connected sum construction for cubical d-polytopes, and apply this construction to certain cubical d-polytopes to conclude that the rays spanned by f-vectors of cubical d-polytopes are dense in Adin's cone. The connectivity result on cubes extends to any product of simplices, and further, it shows the respective realization spaces are contractible.
AB - We prove that the realization space of the d-dimensional cube is contractible. For this we first show that any two realizations are connected by a finite sequence of projective transformations and normal transformations. As an application we use this fact to define an analog of the connected sum construction for cubical d-polytopes, and apply this construction to certain cubical d-polytopes to conclude that the rays spanned by f-vectors of cubical d-polytopes are dense in Adin's cone. The connectivity result on cubes extends to any product of simplices, and further, it shows the respective realization spaces are contractible.
M3 - Conference article
VL - 84B
JO - Seminaire Lotharingien de Combinatoire
JF - Seminaire Lotharingien de Combinatoire
SN - 1286-4889
M1 - 80
T2 - 32nd Conference on Formal Power Series and Algebraic Combinatorics (
Y2 - 6 July 2020 through 24 July 2020
ER -
ID: 257708934