1549055384-Symplectic_Geometry_and_Topology__Eliashberg_

LECTURE 3. FLOER HOMOLOGY 187 3.8. Floer homology revisited It is useful to introduce a covering of the space .CM of contractibl ...

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LECTURE 4 Gromov Compactness and Stable Maps The purpose of this lecture is to discuss how Gromov compactness for J-holo- morphi ...

190 D. SALAMON, FLOER HOMOLOGY then u" has a convergent subsequence. More precisely, the subsequence can be chosen to converge u ...

LECTURE 4. GROMOV COMPACTNESS AND STABLE MAPS 191 This implies that there can be only finitely many points z 1 , ... , ze near w ...

192 D. SALAMON, FLOER HOMOLOGY ( d) For every j, (38) m(zj) = R~lim lim oo v-.oo E(vj, BR)· (39) (e) If the limit curve Vj is co ...

LECTURE 4. GROMOV COMPACTNESS AND STABLE MAPS 193 to at least three other curves in the tree (at distinct points). This conditio ...

194 D. SALAMON, FLOER HOMOLOGY For future reference it is useful to introduce some notation. For every pair a, f3 E T with a =/= ...

LECTURE 4. GROMOV COMPACTNESS AND STABLE MAPS 195 every complex automorphism of the 2-sphere has the form of a fractional linear ...

196 D. SALAMON, FLOER HOMOLOGY (ii) If a.,{3 ET with a.E{3 then (cp~)-^1 o cp~ converges to Zcxf3, uniformly on compact subsets ...

LECTURE 4. GROMOV COMPACTNESS AND STABLE MAPS 197 The topology can be recovered from the collection C of convergent sequences, a ...

198 D. SALAMON, FLOER HOMOLOGY Corollary 4.11. Mo,k,A(M, J) is a compact metrizable space. Proof. By Theorem 4.10, each point in ...

LECTURE 4. GROMOV COMPACTNESS AND STABLE MAPS 199 of degree six. Find the limit stable map and prove that Un Gromov converges to ...

200 D. SALAMON, FLOER HOMOLOGY open stratum in Mo,n·^4 We shall use cross ratios to construct an embedding of Mo,n into (5^2 )N ...

LECTURE 4. GROMOV COMPACTNESS AND STABLE MAPS 201 Proposition 4.19. The map Mo,n --t (S^2 )In of Proposition 4.18 is a homeomor- ...

202 D. SALAMON, FLOER HOMOLOGY is independent of the choice of this a. The existence of a is obvious from Step 1. Moreover, if t ...

LECTURE 4. GROMOV COMPACTNESS AND STABLE MAPS 203 point { w I ( z)} I Ein) as smooth functions of the given n - 3 cross ratios. ...

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LECTURE 5 Multi-Valued Perturbations In this lecture we return to the proof of the Arnold conjecture. We shall assume throughout ...

206 D. SALAMON, FLOER HOMOLOGY Let us now fix a smooth time dependent Hamiltonian Ht = Ht+I : M ___. JR and consider a sequence ...