2006/08/01 by Victor Bangert, Mikhail G. Katz, Bangert, Victor +5
Mathematics · #17B25 (Secondary) #53C23 (Primary) 55R37 #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #math.AT #math.DG #msc:17B25 #msc:53C23 #msc:55R37
paper · pdf · doi:10.48550/arxiv.math/0608006
32 pages
arxiv created 2008/01/03 · arxiv updated 2009/12/01
We study optimal curvature-free inequalities of the type discovered by C. Loewner and M. Gromov, using a generalisation of the Wirtinger inequality for the comass. Using a model for the classifying space BS3 built inductively out of BS1, we prove that the symmetric metrics of certain two-point homogeneous manifolds turn out not to be the systolically optimal metrics on those manifolds. We point out the unexpected role played by the exceptional Lie algebra E7 in systolic geometry, via the calculation of Wirtinger constants. Using a technique of pullback with controlled systolic ratio, we calculate the optimal systolic ratio of the quaternionic projective plane, modulo the existence of a Joyce manifold with Spin(7) holonomy and unit middle-dimensional Betti number.