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Page 1:
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Page 4 and 5:
5.8 Non-local boundary conditions .
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M into Λ(M) as the space of consta
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and converging to Hamiltonian orbit
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1.2 The Chas-Sullivan loop product
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1.1. Remark. The loop product was d
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2.2 Functoriality Let (M1, g1) and
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The orbits of −grad(f1 ⊕f2) are
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this intersection is a finite set o
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(L0) Ω every solution γ ∈ P
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transverse to the stable manifold o
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2.7. Proposition. The homomorphism
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A submanifold L ⊂ T ∗ M is call
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The L 2 -negative gradient equation
Page 30 and 31:
The Riemann surface Σ Ω Υ s = 0
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In the periodic case, we consider H
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3.6. Definition. The Maslov index
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The Riemann surface ΣG is obtained
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3.12. Proposition. For a generic ch
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The following compactness statement
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4.2. Proposition. For a generic cho
Page 44 and 45:
A standard gluing argument shows th
Page 46 and 47:
In the following two sections we wi
Page 48 and 49:
We shall apply the above lemma to t
Page 50 and 51:
Since the inclusion c : M ֒→ Λ
Page 52 and 53:
4.5 The right-hand square is homoto
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commute. Our first aim in this sect
Page 56 and 57:
Moreover, �Dαn(βnvn)�0,p;Ê
Page 58 and 59: We identify the product T ∗Ên ×
Page 60 and 61: Up to multiplying u by U, we can re
Page 62 and 63: The symbol C∞ S ,c indicates boun
Page 64 and 65: 5.11. Theorem. (Cauchy-Riemann oper
Page 66 and 67: 5.15. Lemma. Let p > 1 and α ∈Ê
Page 68 and 69: Proof. By Proposition 5.14 the oper
Page 70 and 71: Then ind∂A = ind∂A1 + ind∂A1.
Page 72 and 73: (V0, . . . , Vk), by V ′ the (k
Page 74 and 75: is bounded and Fredholm of index in
Page 76 and 77: so the transversality hypotheses of
Page 78 and 79: 5.9 Coherent orientations As notice
Page 80 and 81: compact subsets of Σ Ω Υ , for
Page 82 and 83: where Ã(z) = CA(z)C ⊕ A(z), C de
Page 84 and 85: By the additivity property of the M
Page 86 and 87: The space M Υ GE . Let x1 ∈ P(H1
Page 88 and 89: The space M Θ Φ . Let γ ∈ PΘ
Page 90 and 91: The embedding Q ֒→ÊN induces an
Page 92 and 93: Given periodic orbits x1 ∈ P(H1),
Page 94 and 95: Since u and ∂u are integrable ove
Page 96 and 97: with non-local boundary conditions
Page 98 and 99: to ũ0 uniformly on Σ, we may loca
Page 100 and 101: we see that associating ũ to u pro
Page 102 and 103: The energy of a solution u ∈ M K
Page 104 and 105: Since we have applied a conformal r
Page 106 and 107: 6.9. Lemma. There exists a positive
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