Neurology Mathematics Ideas80.pdf - L = LX that can appear as the outer boundary of a fillable disk D = DX of some type X as introduced in Definition

# Neurology Mathematics Ideas80.pdf - L = LX that can appear...

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L = L X that can appear as the outer boundary of a fillable disk D = D X of some type X , as introduced in Definition 5.10. We have already seen that there exists a unique fillable disk D tad X with outer boundary L such that each inner boundary circle of D tad X is a tadpole circle (see the picture (5.39)). In Appendix C.2 we construct explicitly a canonical isomorphism ϕ D : T fine ( D )( ( D )) = −−→ T fine ( D tad X )( ( D tad X )) . (5.44) Our construction of this isomorphism makes use of a combinatorial datum, namely a spanning tree for the graph Γ D that has as edges those defect lines of D that come from X , and as vertices the end points of these defect lines on D together with the inner boundary circles of D . But as we show in Lemma C.9 in the appendix, the isomorphism (5.44) does not depend on this datum. Having obtained the isomorphisms (5.44) we can define the desired isomorphism between the block functors for any two fillable disks D and D of the same type X (and thus in particular

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• Fall '17