Let $(X,\omega)$ be a symplectic manifold and $L\subset X$ be a Lagrangian subspace.
Let $\mu_L:H_2(X,L;\mathbb{Z})\to \mathbb{Z}$ be the *Maslov index*
homomorphism.

**Usual hypothesis**

Recall that $L$ is said to be *monotone*, if there exists $c>0$ such that the following identity holds for all $\beta\in \pi_2(X,L)$:
$$c \mu_L(\beta)=\omega(\beta).$$
The *minimal Maslov number* is defined to be:
$$\inf \{\mu_L(\beta) \ |\ \beta\in \pi_2(X,L), \ \omega(\beta)>0 \}.$$
Now given two *monotone* Lagrangians $L_0,L_1$ call assumption $A1$
$$(A1): \text{the minimal Maslov number of $L_0$ and $L_1$ are strictly greater than 2}$$
and assumption $A2$
$$(A2): \text{ $L_0$ is Hamiltonian isotopic to $L_1$}\phantom{aaaaaaaaaaaaaaaaaaaaaaaaaaaa}$$

In defining Lagrangian intersection Floer homology groups $HF(L_0,L_1)$ usually $A1$ or $A2$ is assumed.

**how are these assumption exploited in the construction of the homology?**and what's the role of**monotonicity**?- Why assuming the Lagrangians to be
**spin**it is said to simplify things? How can we use the spin assumption?