Table1:LegendrianLinks Link Topological ... - Duke University

Table 1: Legendrian Links

Link Topological Cromwell(𝑡𝑏1, 𝑡𝑏2)

Legendrian TBType Switch? Diagram Switch? Polyhedron

L2a1 ✓ (−1,−1) ✓ -3 -2 -1 0

L4a1 ✓ (−1,−1) ✓ -3 -2 -1 0

m(L4a1) ✓ (−2,−2) ✓ -4 -3 -2 -1 0

(−3,−1) -

L5a1 ✓ (−3,−2) - -5 -4 -3 -2 -1 0

(−4,−1) -

m(L5a1) ✓ (−1,−1) ✓ -3 -2 -1 0

L6a1 ✓ (−1,−1) ✓ -3 -2 -1 0

(−1,−1) ✓

m(L6a1) ✓(−3,−3) ✓ -6 -5 -4 -3 -2 -1 0

(−4,−2) -

(−5,−1) -

L6a2 ✓ (−2,−2) ✓ -4 -3 -2 -1 0

(−3,−1) -

L6a3 ✓(−3,−3) ✓ -6 -5 -4 -3 -2 -1 0

(−3,−3) ✓

(−4,−2) -

(−5,−1) -

m(L6a3) ✓ (−1,−1) ✓ -3 -2 -1 0

L7a1 ✗(−1,−2) - -3 -2 -1 0

(−2,−1) -

m(L7a1) ✗

(−3,−3) - -6 -5 -4 -3 -2 -1 0

(−4,−2) -

(−5,−1) -

L7a2 -(−6,−1) - -7 -6 -5 -4 -3 -2 -1 0

(−6,−1) -

m(L7a2) -

(1,−3) - -2 -1 0 1 2

(0,−2) -

(−1,−1) -

L7a3 - (1,−1) - -1 0 1 2

m(L7a3) -

(−6,−3) - -9 -8 -7 -6 -5 -4 -3 -2 -1 0

(−7,−2) -

(−8,−1) -

L7a4 ✓ (−1,−1) ✓ -3 -2 -1 0

(−1,−1) ✓

m(L7a4) ✓(−4,−3) - -7 -6 -5 -4 -3 -2 -1 0

�(−5,−2) -

(−6,−1) -

L7a5 ✓ (−3,−2) - -5 -4 -3 -2 -1 0

(−4,−1) -

m(L7a5) ✓(−2,−2) ✗?11 -4 -3 -2 -1 0

(−2,−2) ✗?10

(−3,−1) -

L7a6 ✓ (−1,−1) ✗ -3 -2 -1 0

m(L7a6) ✓

(−4,−3) - -7 -6 -5 -4 -3 -2 -1 0

�(−4,−3) -

(−5,−2) -

(−6,−1) -

L7n1 - (−6,−1) - -7 -6 -5 -4 -3 -2 -1 0

m(L7n1) - (1,−1) - -1 0 1 2

L7n2 - (−6,−1) - -7 -6 -5 -4 -3 -2 -1 0

m(L7n2) - (1,−1) - -1 0 1 2

L8n1 -(−3,−1) - -4 -3 -2 -1 0

(−3,−1) -

m(L8n1) - (−3,−1) - -4 -3 -2 -1 0

L8n2 - (−3,−1) - -4 -3 -2 -1 0

m(L8n2) - (−3,−1) - -4 -3 -2 -1 0

L9n1 - (−8,−1) - -9 -8 -7 -6 -5 -4 -3 -2 -1 0

m(L9n1)- (1,−1) - 0 1 2

(1,−1) -

L9n2 - (−8,−1) - -9 -8 -7 -6 -5 -4 -3 -2 -1 0

m(L9n2)- (1,−1) - 0 1 2

(1,−1) -

L9n3 - (−8,−1) - -9 -8 -7 -6 -5 -4 -3 -2 -1 0

m(L9n3)- (1,−1) - 0 1 2

(1,−1) -

L9n4- (−10,−1) - -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0

(−10,−1) -

m(L9n4) - (3,−1) - 0 1 2 3 4

L9n5- (−10,−1) - -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0

(−10,−1) -

m(L9n5) - (3,−1) - 0 1 2 3 4

L9n6- (−10,−1) - -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0

(−10,−1) -

m(L9n6) - (3,−1) - 0 1 2 3 4

L9n7- (−8,−1) - -9 -8 -7 -6 -5 -4 -3 -2 -1 0

(−8,−1) -

m(L9n7)- (1,−1) - 0 1 2

(1,−1) -

L9n8- (−8,−1) - -9 -8 -7 -6 -5 -4 -3 -2 -1 0

(−8,−1) -

m(L9n8)- (1,−1) - 0 1 2

(1,−1) -

L9n9 - (−8,−1) - -9 -8 -7 -6 -5 -4 -3 -2 -1 0

m(L9n9) - (1,−1) - 0 1 2

L9n10 ✗(−1,−1) - -3 -2 -1 0

(−1,−1) -

m(L9n10) ✗

(−3,−4) - -7 -6 -5 -4 -3 -2 -1 0

(−4,−3) -

(−5,−2) -

m(L9n10)

(−5,−2) -

(−6,−1) -

L9n11 ✗(−3,−2) -

(−4,−1) -

m(L9n11) ✗

(−1,−3) - -4 -3 -2 -1 0

(−1,−3) -

(−2,−2) -

(−3,−1) -

L9n12 - (3,−1) - 0 1 2 3 4

m(L9n12) - (−10,−1) - -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0

L9n13 ✓(−3,−3) ✗?10 -6 -5 -4 -3 -2 -1 0

(−4,−2) -

(−5,−1) -

m(L9n13) ✓ (−2,−1) - -3 -2 -1 0

L9n14 -

(1,−3) - -2 -1 0 1 2

(0,−2) -

(−1,−1) -

m(L9n14) - (−6,−1) - -7 -6 -5 -4 -3 -2 -1 0

L9n15- (−7,−1) - -8 -7 -6 -5 -4 -3 -2 -1 0

(−6,−2) -

m(L9n15) - (1,−1) - 0 1 2

L9n16 -(1,−3) - -2 -1 0 1 2

(0,−2) -

(−1,−1) -

m(L9n16) - (−6,−1) - -7 -6 -5 -4 -3 -2 -1 0

L9n17 -

(−6,−3) - -9 -8 -7 -6 -5 -4 -3 -2 -1 0

(−7,−2) -

(−8,−1) -

m(L9n17)- (1,−1) - 0 1 2

(1,−1) -

L9n18✓ (−3,−3) ✓ -8 -7 -6 -5 -4 -3 -2 -1 0

(−5,−2) -

m(L9n18) ✓ (−1,−1) ✓ -3 -2 -1 0

L9n19✗ (−1,−3) - -6 -5 -4 -3 -2 -1 0

(−3,−2) -

L10n23 - (3,−1) - 0 1 2 3 4

m(L10n23) - (−10,−1) - -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0

L10n24 ✗(−3,−1) - -4 -3 -2 -1 0

(−2,−3) -

m(L10n24) ✗

(−1,−4) - -5 -4 -3 -2 -1 0

(−1,−4) -

(−2,−3) -

(−3,−2) -

(−4,−1) -

L10n34 - (1,−1) - 0 1 2

m(L10n34) -(−6,−3) - -9 -8 -7 -6 -5 -4 -3 -2 -1 0

(−7,−2) -

(−8,−1) -

L10n42 -(1,−1) - 0 1 2

(1,−1) -

m(L10n42) -(−6,−3) - -9 -8 -7 -6 -5 -4 -3 -2 -1 0

(−7,−2) -

(−8,−1) -

L10n44 ✓

(−4,−3) - -7 -6 -5 -4 -3 -2 -1 0

�(−4,−3) -

(−5,−2) -

(−6,−1) -

m(L10n44) ✓ (−1,−1) ✗?10 -3 -2 -1 0

L10n45 -(−3,−2) - -5 -4 -3 -2 -1 0

(−4,−1) -

m(L10n45) -(−3,−1) - -4 -3 -2 -1 0

(−3,−1) -

L10n46 - (−3,−1) - -4 -3 -2 -1 0

L10n54 ✓ (−1,−1) ✗?10 -3 -2 -1 0

m(L10n54) ✓ (−4,−3) - -9 -8 -7 -6 -5 -4 -3 -2 -1 0

L10n56 ✗(−4,−3) -

(−6,−2) -

m(L10n56) ✗ (−1,−1) - -3 -2 -1 0

L10n57 ✗(−4,−1) -

(−3,−2) -

m(L10n57) ✗ (−3,−1) - ?

L11n119 - (3,−1) - 0 1 2 3 4

m(L11n119) - (−10,−1) - -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0

L11n132 - (−10,−1) - -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0

m(L11n132) -(3,−1) - 0 1 2 3 4

(3,−1) -

L11n133 - (−10,−1) - -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0

m(L11n133) - (3,−1) - 0 1 2 3 4

L11n139 -(1,−1) - 0 1 2

(1,−1) -

m(L11n139) - (−8,−1) - -9 -8 -7 -6 -5 -4 -3 -2 -1 0

L11n140 - (−8,−1) - -9 -8 -7 -6 -5 -4 -3 -2 -1 0

m(L11n140) -

(1,−1) - 0 1 2

(1,−1) -

L11n148 - (1,−1) - 0 1 2

m(L11n148) - (−8,−1) - -9 -8 -7 -6 -5 -4 -3 -2 -1 0

L11n204- (−6,−3) - -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0

(−7,−2) -

m(L11n204) - (1,−1) - 0 1 2

L11n205 - (−6,−1) - -7 -6 -5 -4 -3 -2 -1 0

m(L11n205) - (1,−3) - -4 -3 -2 -1 0 1 2

L11n218 -(1,−3) -

(−1,−2) -

m(L11n218) - (−6,−1) - -7 -6 -5 -4 -3 -2 -1 0

L11n219 - (1,−3) - ?

m(L11n219) - (−6,−1) - -7 -6 -5 -4 -3 -2 -1 0

L11n226 - (−6,−3) - ?

m(L11n226) - (1,−1) - 0 1 2

Table1:LegendrianLinks Link Topological ... - Duke University

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