E_7, Wirtinger inequalities, Cayley 4-form, and homotopy
摘要
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 BS^3 built inductively out of BS^1, 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 E_7 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.
引用
@article{arxiv.math/0608006,
title = {E_7, Wirtinger inequalities, Cayley 4-form, and homotopy},
author = {Victor Bangert and Mikhail G. Katz and Steven Shnider and Shmuel Weinberger},
journal= {arXiv preprint arXiv:math/0608006},
year = {2008}
}
备注
32 pages