On the realization space of the cube

Institut for Matematiske Fag

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Standard

On the realization space of the cube. / Adiprasito, Karim; Kalmanovich, Daniel; Nevo, Eran.

I: Journal of the European Mathematical Society, Bind 26, Nr. 1, 2024, s. 261-273.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Adiprasito, K, Kalmanovich, D & Nevo, E 2024, 'On the realization space of the cube', Journal of the European Mathematical Society, bind 26, nr. 1, s. 261-273. https://doi.org/10.4171/JEMS/1361

APA

Adiprasito, K., Kalmanovich, D., & Nevo, E. (2024). On the realization space of the cube. Journal of the European Mathematical Society, 26(1), 261-273. https://doi.org/10.4171/JEMS/1361

Vancouver

Adiprasito K, Kalmanovich D, Nevo E. On the realization space of the cube. Journal of the European Mathematical Society. 2024;26(1):261-273. https://doi.org/10.4171/JEMS/1361

Author

Adiprasito, Karim ; Kalmanovich, Daniel ; Nevo, Eran. / On the realization space of the cube. I: Journal of the European Mathematical Society. 2024 ; Bind 26, Nr. 1. s. 261-273.

Bibtex

@article{9f061003e6094fb3bd6844589488dceb,

title = "On the realization space of the cube",

abstract = "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 that the respective realization spaces are contractible. ",

keywords = "connected sum, Cubical polytopes, face numbers, realization space",

author = "Karim Adiprasito and Daniel Kalmanovich and Eran Nevo",

note = "Publisher Copyright: {\textcopyright} 2023 European Mathematical Society.",

year = "2024",

doi = "10.4171/JEMS/1361",

language = "English",

volume = "26",

pages = "261--273",

journal = "Journal of the European Mathematical Society",

issn = "1435-9855",

publisher = "European Mathematical Society Publishing House",

number = "1",

}

RIS

TY - JOUR

T1 - On the realization space of the cube

AU - Adiprasito, Karim

AU - Kalmanovich, Daniel

AU - Nevo, Eran

PY - 2024

Y1 - 2024

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 that 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 that the respective realization spaces are contractible.

KW - connected sum

KW - Cubical polytopes

KW - face numbers

KW - realization space

U2 - 10.4171/JEMS/1361

DO - 10.4171/JEMS/1361

M3 - Journal article

AN - SCOPUS:85186641427

VL - 26

SP - 261

EP - 273

JO - Journal of the European Mathematical Society

JF - Journal of the European Mathematical Society

SN - 1435-9855

IS - 1

ER -

ID: 390929681