Manuscript XV-B@2 · XV-B.tex · definition · 4d3f12e8

Definition: Relative obstruction

Reconstruction and the exact relative-lifting criterion › Specified affine corrections · lines 425–446

XV-B@2#def:obstruction, XV-B@2#eq:obstruction

Fix a preliminary lift $F_{0}$ and a vector subspace

A \subset Hom (P_{int}, Y) .

The candidate family is $F_{0} + A$ . Define

\partial : A ⟶ Hom (H, Y), \partial a = a ∣_{H} .

Since $c ∣_{H} = 0$ , the null defect

d_{0} = F_{0} ∣_{H}

takes values in $Y$ . Its relative obstruction is

Ob_{A} (F_{0}) = [d_{0}] \in Hom (H, Y) / \partial A .

Displayed formulas in this passage

XV-B@2#eq:obstruction · line 441
$Ob_{A} (F_{0}) = [d_{0}] \in Hom (H, Y) / \partial A .$
unlabeled · line 428
$A \subset Hom (P_{int}, Y) .$
unlabeled · line 432
$\partial : A ⟶ Hom (H, Y), \partial a = a ∣_{H} .$
unlabeled · line 437
$d_{0} = F_{0} ∣_{H}$