ScalingStacks

The map $\Psi_{I\times Y;\Delta_{+},\alpha^{\prime}}$ is now easy to describe. It is induced by capping $J$ with a disk, so it only affects the factor $\operatorname{KhR}_{N}(J)$, in a standard way. Precisely, we have

(11)

$$\Psi_{I\times Y;\Delta_{+},\alpha^{\prime}}(v\otimes X^{n})=\begin{cases}v&\text{if }n=N-1,\\ 0&\text{if }n=0,1,\dots,N-2,\end{cases}$$

for all $v\in\underline{\mathcal{S}\mkern-3.0mu}\mkern 3.0mu_{0}^{N,\alpha}(W_{1};K,L)$.