Title: The Proportionality Principle of Simplicial Volume
Authors: Clara Strohm (=Clara Löh)

Email: strohm@math.uni-muenster.de
Address: Einsteinstr. 62, 48143 Münster, Germany

MSC: 57R19, 55N35
Abstract:
The simplicial volume is a homotopy invariant of oriented closed 
connected manifolds measuring the efficiency of representing the 
fundamental class by singular chains with real coefficients. Despite of 
its topological nature, the simplicial volume is linked to Riemannian 
geometry in various ways, e.g., by the proportionality principle. The 
proportionality principle of simplicial volume states that the 
simplicial volume and the Riemannian volume are proportional for 
oriented closed connected Riemannian manifolds sharing the same 
universal Riemannian covering. Thurston indicated a proof of the 
proportionality principle using his (smooth) measure homology. It is the 
purpose of this diploma thesis to provide a full proof of the 
proportionality principle based on Thurston's approach. In particular, 
it is shown that (smooth) measure homology and singular homology are 
isometrically isomorphic for all smooth manifolds. This implies that the 
simplicial volume indeed can be computed in terms of measure homology. 

Included eps files: fg.eps, dragon_schoon.eps