CConstruction of a parallelizationIn this appendix we provide details of the construction of a parallelization Π for the collectionof relative block functors for all fine refinements, as defined in Definition 5.16(ii).C.1Isomorphisms among block functors of fillable disksAs a preparatory step we restrict our attention to a specific class of defect surfaces, namelyfillable disks, and construct a distinguished isomorphism between the block functors for anytwo such disks of the same type. Recall from Definition 5.10 that a fillable disk of typeXisa defect surfaceDXtogether with a setδtrof transparent defect lines and with a distinguishedboundary segment∂outer, called theouter boundaryofDX. The removal ofδtrfromDXgives adefect surface for which every gluing circle and gluing interval except for∂outeris fillable by adisk in the sense of Definition 5.4, and the corresponding filling ofDX\δtryields a defect surfaceXwith underlying surface being a disk and with
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- Fall '17
