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reference request – Lagrangian Floer Homology Answer

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reference request – Lagrangian Floer Homology

I’ve been beginning to find out about Lagrangian Floer Homology utilizing these notes https://arxiv.org/pdf/1701.02293.pdf.

Now on web page $16$ have been we’re working within the common protecting of the related part of the area $ mathcal{P}(gamma,L_0,L_1)$ the creator begins speaking about riemannian metrics and the tangent area . Now a priori this appears to me to breathe an infinite-dimensional area so I am unable to simply employ the regular definition of tangent area. Then I thought of utilizing the definition of tangent area that Milnor in his bespeak Morse principle introduces for the area $Omega(M,p,q)$ however plane so we’re working within the uinversal protecting of an alalogue of this earlier area. From what the creator is doing evidently a tangent vector there’s a household of tangent vectors that reckon on $t$, however I’m not positive if that is undoubted and after that how we will employ this definition to compute differentials of the map $mathcal{A}$.

Or perhaps I can employ the intuitively thought {that a} area and it is protecting have isomorphic tangent areas so I can simply employ Milnor’s definition. However I’m not positive how can I compute the differential utilizing this definition , for I do not fairly behold what’s the round of the area, is it $pi^{-1}circ c(s)$
, the place now we have $pi$ in a neighborhood the place it is a homeomorphisms and $c$ is a round within the loop area that can give the vector bailiwick alongside the round ?

Does anybody know a unique reference for this or can enlighten me ?

Thanks in forward.

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