Neurology Mathematics Ideas118.pdf - C Construction of a parallelization In this appendix we provide details of the construction of a parallelization \u03a0

Neurology Mathematics Ideas118.pdf - C Construction of a...

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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 segmentouter, called theouter boundaryofDX. The removal ofδtrfromDXgives adefect surface for which every gluing circle and gluing interval except forouteris 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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