Manuscript VI-B@1 · VI-B-v1.tex · section · 33798723

The initial-surface-preserving gauge group

The second-order Einstein–scalar coefficient space › The initial-surface-preserving gauge group · lines 622–638

VI-B@1#eq:gauge

Let

g = C_{c}^{\infty} (D_{R, b}^{\circ}; T D_{R, b}),

and define formal pullbacks

F_{ξ, ζ}^{*} = exp (κ L_{ξ} + κ^{2} L_{ζ}) (mod κ^{3}), ξ, ζ \in g .

The generators vanish near $Σ_{0}$ and near the lateral boundary. Their formal compositions again have compact generators, by the truncated Baker–Campbell–Hausdorff formula.

Displayed formulas in this passage

VI-B@1#eq:gauge · line 629
$F_{ξ, ζ}^{*} = exp (κ L_{ξ} + κ^{2} L_{ζ}) (mod κ^{3}), ξ, ζ \in g .$
unlabeled · line 625
$g = C_{c}^{\infty} (D_{R, b}^{\circ}; T D_{R, b}),$

Nearby in this section

proposition: Proposition: Full coefficient action
section: The initial-surface-preserving gauge group