On the realization space of the cube
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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.
Originalsprog | Engelsk |
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Tidsskrift | Journal of the European Mathematical Society |
Vol/bind | 26 |
Udgave nummer | 1 |
Sider (fra-til) | 261-273 |
ISSN | 1435-9855 |
DOI | |
Status | Udgivet - 2024 |
Bibliografisk note
Funding Information:
Funding. The first author acknowledges support by Horizon Europe ERC Grant number 101045750, Project acronym: HodgeGeoComb. The second and third authors acknowledge support by ISF grants 1695/15 and 2480/20 and by ISF-BSF joint grant 2016288.
Publisher Copyright:
© 2023 European Mathematical Society.
ID: 390929681