(Floer products involving the identity) We wish to heuristically explain a special case relevant to Joyce-Imagi-Santos (cf. section 2.3), concerning the geometric interpretation of the Floer product mod 2

$$HF^{0}(L^{\prime},L)\otimes HF^{0}(L,L^{\prime})\to HF^{0}(L,L).$$

Here $L,L^{\prime}$ are assumed to be transverse. Hamiltonian invariance means we can alternatively think of

$$HF^{0}(L^{\prime},\phi_{\epsilon H}(L))\otimes HF^{0}(L,L^{\prime})\to HF^{0}(L,\phi_{\epsilon H}(L)).$$

This is defined by the count of holomorphic triangles with input corners at $CF^{0}(L,L^{\prime})$, $CF^{0}(L^{\prime},\phi_{\epsilon H}(L))$, and an output corner at $CF^{0}(L,\phi_{\epsilon H}(L))$. We may assume the Morse function $H|_{L}$ has only one maximum point $r$ on $L$, which represents the unit of $HF^{*}(L,L)$. When $\epsilon\to 0$, then $L$ and $\phi_{\epsilon H}(L)$ coincide, and the holomorphic triangles become holomorphic strips with ends at $CF^{0}(L,L^{\prime})$, $CF^{0}(L^{\prime},L)$ (alternatively seen as a degree $n$ output) and passing through the point $r\in L$. This last incidence condition is independent of the position of $r$ on $L$, since we can choose $H$ to have its maximum at any generic prescribed point. Notice in this strip interpretation, there is no longer any Hamiltonian perturbation. This interpretation featured in Lemma 2.7.