Neurology Mathematics Ideas125.pdf - Example C.6 Consider the fillable disk 1 1 D = M 2(C.25 A 0 Using Equation(3.45 and Lemma 3.17 we obtain \u2127D = \u223c

Neurology Mathematics Ideas125.pdf - Example C.6 Consider...

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Example C.6. Consider the fillable disk A 2 M 0 1 1 D = (C.25) Using Equation (3.45) and Lemma 3.17 we obtain D = integraldisplay m ∈M T [0] ( m D A ) m = integraldisplay m ∈M integraldisplay a ∈A a .m D. [3] a m = integraldisplay m ∈M integraldisplay a ∈A a .m a m = integraldisplay m ∈M integraldisplay a ∈A m a a.m. (C.26) We have actually already encountered the defect one-manifold that constitutes the outer bound- ary of the disk D : it is the defect circle I ւ κ ( M ) in (5.14) with framing index κ = 0. Similarly we obtain the following list of defect one-manifolds and silent objects for all other transparent disks with outer boundaries given by one of the circles (5.14): I ր κ ( M ) : = integraldisplay m ∈M integraldisplay a ∈A m m.a [ κ 1] a = integraldisplay m ∈M integraldisplay a ∈A m m.a [ κ 1] a, I ւ κ ( M ) : = integraldisplay m ∈M integraldisplay a ∈A m a a [ κ ] .m, I տ κ ( M ) : = integraldisplay m ∈M integraldisplay a ∈A m a [ κ 1] a.m, I ց κ ( M ) :
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