# sg.symplectic geometry – Constant holomorphic strips in Lagrangian floer cohomology

Let $$(P,omega)$$ be a symplectic manifold , when defining the lagrangian floer cohomology of a pair $$(L_0,L_1)$$ of lagrangian submanifolds with $$Sigma_{L}geq 3$$ we will want to look at the space $$mathcal{M}_{J}(x,y)$$ ,where $$x,yin L_0cap L_1$$, of $$J$$-holomorphic strips connecting intersection points and satisfying a sobolev condition, namely that $$uin W^{k,2}(mathbb{R}times (0,1), P)$$ for $$k>1$$. Now if we had $$x=y$$ will the constant strip be an element of $$mathcal{M}_{J}(x,x)$$? I would say no since we want the paths in this space to satisfy a sobolev in condition ,and in particular the constant path will not satisfy it , but I wanted to make sure this reasoning is correct.

Any enlightment is appreciated , thanks in advance.