Transcendental simplicial volumes

2019/11/14 by Heuer, Nicolaus, Loeh, Clara
#03D78 #11J86 #20J05 #57M07 #57N65 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1911.06386

Abstract

We show that there exist closed manifolds with arbitrarily small transcendental simplicial volumes. Moreover, we exhibit an explicit uncountable family of (transcendental) real numbers that are not realised as the simplicial volume of a closed manifold.

Related

• The spectrum of simplicial volume of non-compact manifolds
• The simplicial volume of contractible 3-manifolds
• Odd manifolds of small integral simplicial volume
• Cubical simplicial volume of 3-manifolds
• The spectrum of simplicial volume