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Jan 29, 2012 at 23:42 comment added JHM What I want from this question is a measure which recognizes that "configurations of $2n$ lines in $\mathbb{R}^{2n}$" is different than "configurations of n 2-planes". The volume $|e_1 \wedge \ldots \wedge f_n|$ is insensitive to configurations of 2-planes. The point is to find a form or measure which isn't.
Jan 29, 2012 at 22:36 comment added JHM In my own particular situation this measure is not interesting because all the $e_i, f_i$ generate a unimodular lattice----hence their wedge product is 1. This then does nothing to distinguish them.
Jan 29, 2012 at 21:25 history answered Victor Dods CC BY-SA 3.0