Manuscript XVI-M@1 · XVI-M.tex · section · 7346c909

M.3 Contact space, graph maps, and invisible directions

M.3 Contact space, graph maps, and invisible directions · lines 916–926

coefficient expansion. Because $a ˉ_{b} = χ_{I} a ˉ^_{b}$ , expand the switch-free factor $a ˉ^_{b}^{μν} = \sum_{m} c_{m, b} m$ over coefficient monomials $m = (μν) \otimes (σ -symbol) \otimes (h -symbol)$ ; the output component is part of the monomial. (The overall factor $χ_{I} (w)$ in $a ˉ_{b}$ factors out of the linear algebra on coefficients.) Then

b \in B_{N} \sum a ˉ^_{b} \otimes b = m \sum m \otimes u_{m}, u_{m} := b \sum c_{m, b} b \in H_{4 + N}, U_{N} := span {u_{m}} .

graph_contact_map.txt lists a basis of each $U_{N}$ as vectors $u_{m}$ , labelled by their pivot monomials $m$ .

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unlabeled · line 922
$b \in B_{N} \sum a ˉ^_{b} \otimes b = m \sum m \otimes u_{m}, u_{m} := b \sum c_{m, b} b \in H_{4 + N}, U_{N} := span {u_{m}} .$

M.3 Contact space, graph maps, and invisible directions

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