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- Title
2-LC triangulated manifolds are exponentially many.
- Authors
Benedetti, Bruno; Pavelka, Marta
- Abstract
We introduce "t-LC triangulated manifolds" as those triangulations obtainable from a tree of d-simplices by recursively identifying two boundary .d - 1/-faces whose intersection has dimension at least d - t - 1. The t-LC notion interpolates between the class of LC manifolds introduced by Durhuus and Jonsson (corresponding to the case t D 1), and the class of all manifolds (case t D d). Benedetti and Ziegler proved that there are at most 2d²N triangulated 1-LC d-manifolds with N facets. Here we prove that there are at most 2d/2³ N triangulated 2-LC d-manifolds with N facets. This extends an intuition by Mogami for d D 3 to all dimensions. We also introduce "t -constructible complexes", interpolating between constructible complexes (the case t D 1) and all complexes (case t D d). We show that all t -constructible pseudomanifolds are t-LC, and that all t -constructible complexes have (homotopical) depth larger than d - t. This extends the famous result by Hochster that constructible complexes are (homotopy) Cohen-Macaulay.
- Subjects
QUANTUM gravity; INTUITION
- Publication
Annales de l'Institut Henri Poincaré D, 2024, Vol 11, Issue 2, p363
- ISSN
2308-5827
- Publication type
Article
- DOI
10.4171/AIHPD/170