Rank-3 scale theorems: Difference between revisions
| Line 28: | Line 28: | ||
These are equivalent, since the separating interval can be taken to be g1 and the generator of each chain = g1 + g2. | These are equivalent, since the separating interval can be taken to be g1 and the generator of each chain = g1 + g2. | ||
For theorems relating to the AG property, see [[AG]]. | |||
==== Definitions: LQ ==== | ==== Definitions: LQ ==== | ||
Let n = a_1 + ... + a_r be the scale size, w a scale word with signature a_1 X_1, ..., a_r X_r, let L be a line of the form L(t) = (a_1, ..., a_r)t + v_0, where v_0 is a constant vector in R^r. We say that L is ''in generic position'' if L contains a point (0, α_1, α_2, ... α_{r-1}) where α_i and α_i/α_j for i != j are irrational. | Let n = a_1 + ... + a_r be the scale size, w a scale word with signature a_1 X_1, ..., a_r X_r, let L be a line of the form L(t) = (a_1, ..., a_r)t + v_0, where v_0 is a constant vector in R^r. We say that L is ''in generic position'' if L contains a point (0, α_1, α_2, ... α_{r-1}) where α_i and α_i/α_j for i != j are irrational. | ||