PreprintarXiv licencearXiv
Angle cocycles, Euler characteristic, and simplicial volume of smooth manifolds
Abstract
A celebrated conjecture of Gromov states that for closed aspherical manifolds, the vanishing of simplicial volume implies the vanishing of the Euler characteristic. We prove Gromov's conjecture for closed convex projective manifolds and, more generally, for closed orientable smooth manifolds admitting an immersed straightening. Generalising the straightening of simplices in properly convex domains in real projective space, we introduce the notion of immersed straightening and prove that, for every integer d≥ 1, there exists a constant Cd>0 such that every closed orientable smooth d-manifold M admitting an immersed straightening satisfies |χ(M)|≤ Cd||M||.
Related
- Gromov's Simplicial Volume Vanishing Conjecture for Positive Scalar Curvature
- Positivity of simplicial volume and uniqueness for the twelve-vertex flag three-spheres
- An irregular smooth Fano fourfold in positive characteristic
- Characteristic-free characterizations of projective space for smooth toric varieties
- The Euler characteristic of Pin± manifolds
BibTeX
@misc{bucher2026angle,
title = {{Angle cocycles, Euler characteristic, and simplicial volume of smooth manifolds}},
author = {Michelle Bucher and Stefano Francaviglia and Grazia Rago},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32342},
eprint = {2610.32342},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32342},
}
RIS
TY - UNPB
TI - Angle cocycles, Euler characteristic, and simplicial volume of smooth manifolds
AU - Michelle Bucher
AU - Stefano Francaviglia
AU - Grazia Rago
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32342
UR - https://arxiv.org/abs/2610.32342
AB - A celebrated conjecture of Gromov states that for closed aspherical manifolds, the vanishing of simplicial volume implies the vanishing of the Euler characteristic. We prove Gromov's conjecture for closed convex projective manifolds and, more generally, for closed orientable smooth manifolds admitting an immersed straightening. Generalising the straightening of simplices in properly convex domains in real projective space, we introduce the notion of immersed straightening and prove that, for every integer d≥ 1, there exists a constant C_d>0 such that every closed orientable smooth d-manifold M admitting an immersed straightening satisfies |χ(M)|≤ C_d||M||.
ER -