Manuscript XII-A@2 · XII-A-v2.tex · section · 955d4b22

Kernel maps and contraction stages

Continuity at the named levels › Kernel maps and contraction stages · lines 1400–1418

XII-A@2#eq:contractioncone

For closed cones $Γ_{1} \subset G_{n}$ , $Γ_{2} \subset G_{m}$ over compact input supports, put $N = n + m - 2 k$ . For $N > 0$ , define the unsymmetrized contraction cone by

Γ_{1} \circ_{k} Γ_{2} = {(x, ζ; x^{'}, ζ^{'}) \neq = 0 : \exists y, y^{'}, q \in V_{- σ}^{k}, (x, ζ; y, q) \in Γ_{1} \cup 0_{K_{1}}, (x^{'}, ζ^{'}; y^{'}, - q) \in Γ_{2} \cup 0_{K_{2}}} .

Here $0_{K}$ is the zero section over $K$ . Let $K_{out}$ and $Γ_{out}$ be the finite unions of permutations of the projected support and this cone.

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XII-A@2#eq:contractioncone · line 1405
$Γ_{1} \circ_{k} Γ_{2} = {(x, ζ; x^{'}, ζ^{'}) \neq = 0 : \exists y, y^{'}, q \in V_{- σ}^{k}, (x, ζ; y, q) \in Γ_{1} \cup 0_{K_{1}}, (x^{'}, ζ^{'}; y^{'}, - q) \in Γ_{2} \cup 0_{K_{2}}} .$

Kernel maps and contraction stages

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