E_7, Wirtinger inequalities, Cayley 4-form, and homotopy
| dc.creator | Bangert, Victor | |
| dc.creator | Katz, Mikhail G. | |
| dc.creator | Shnider, Steven | |
| dc.creator | Weinberger, Shmuel | |
| dc.date | 2006-08-01 | |
| dc.date | 2008-01-03 | |
| dc.date.accessioned | 2026-07-07T08:52:13Z | |
| dc.date.available | 2026-07-07T08:52:13Z | |
| dc.description | 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. | |
| dc.description | 32 pages | |
| dc.identifier | https://arxiv.org/abs/math/0608006 | |
| dc.identifier | http://arxiv.org/abs/math/0608006 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/145207 | |
| dc.subject | Differential Geometry | |
| dc.subject | Algebraic Topology | |
| dc.subject | 53C23 (Primary) 55R37, 17B25 (Secondary) | |
| dc.title | E_7, Wirtinger inequalities, Cayley 4-form, and homotopy | |
| dc.type | text |