Homological invariance for asymptotic invariants and systolic inequalities. (English) Zbl 1160.53021

Brunnbauer, Michael

Geom. Funct. Anal. 18, No. 4, 1087-1117 (2008).

It is proved that certain asymptotic and systolic invariants of a connected, closed smooth manifold depend only on the image of the fundamental class under the classifying map of the universal covering. These invariants include the minimal volume entropy, the spherical volume and the systolic constant. The systolic constant of a manifold with fundamental group of order two is computed, and an inequality between the minimal volume entropy and the systolic constant is derived.

Reviewer: József Szilasi (Debrecen)

MSC:

53C22	Geodesics in global differential geometry
53C23	Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
53C20	Global Riemannian geometry, including pinching
57R19	Algebraic topology on manifolds and differential topology

Keywords:

systolic constant; minimal volume entropy; spherical volume