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Page 1: Georgia Institute of Technologypeople.math.gatech.edu/~etnyre/TechTopology/2014/Dun...tetrahedra! 500 0 500 1000 1500 2000 2500 volume! 500 0 500 1000 1500 2000 2500 slope=0.901 intercept=3.229
Page 2: Georgia Institute of Technologypeople.math.gatech.edu/~etnyre/TechTopology/2014/Dun...tetrahedra! 500 0 500 1000 1500 2000 2500 volume! 500 0 500 1000 1500 2000 2500 slope=0.901 intercept=3.229
Page 3: Georgia Institute of Technologypeople.math.gatech.edu/~etnyre/TechTopology/2014/Dun...tetrahedra! 500 0 500 1000 1500 2000 2500 volume! 500 0 500 1000 1500 2000 2500 slope=0.901 intercept=3.229
Page 4: Georgia Institute of Technologypeople.math.gatech.edu/~etnyre/TechTopology/2014/Dun...tetrahedra! 500 0 500 1000 1500 2000 2500 volume! 500 0 500 1000 1500 2000 2500 slope=0.901 intercept=3.229
Page 5: Georgia Institute of Technologypeople.math.gatech.edu/~etnyre/TechTopology/2014/Dun...tetrahedra! 500 0 500 1000 1500 2000 2500 volume! 500 0 500 1000 1500 2000 2500 slope=0.901 intercept=3.229
Page 6: Georgia Institute of Technologypeople.math.gatech.edu/~etnyre/TechTopology/2014/Dun...tetrahedra! 500 0 500 1000 1500 2000 2500 volume! 500 0 500 1000 1500 2000 2500 slope=0.901 intercept=3.229
Page 7: Georgia Institute of Technologypeople.math.gatech.edu/~etnyre/TechTopology/2014/Dun...tetrahedra! 500 0 500 1000 1500 2000 2500 volume! 500 0 500 1000 1500 2000 2500 slope=0.901 intercept=3.229
Page 8: Georgia Institute of Technologypeople.math.gatech.edu/~etnyre/TechTopology/2014/Dun...tetrahedra! 500 0 500 1000 1500 2000 2500 volume! 500 0 500 1000 1500 2000 2500 slope=0.901 intercept=3.229

0

50 crossings:

Page 9: Georgia Institute of Technologypeople.math.gatech.edu/~etnyre/TechTopology/2014/Dun...tetrahedra! 500 0 500 1000 1500 2000 2500 volume! 500 0 500 1000 1500 2000 2500 slope=0.901 intercept=3.229

0 Simpli�ed: 41

Page 10: Georgia Institute of Technologypeople.math.gatech.edu/~etnyre/TechTopology/2014/Dun...tetrahedra! 500 0 500 1000 1500 2000 2500 volume! 500 0 500 1000 1500 2000 2500 slope=0.901 intercept=3.229

0

100 crossings:

Page 11: Georgia Institute of Technologypeople.math.gatech.edu/~etnyre/TechTopology/2014/Dun...tetrahedra! 500 0 500 1000 1500 2000 2500 volume! 500 0 500 1000 1500 2000 2500 slope=0.901 intercept=3.229

0

Simpli�ed: 81

Page 12: Georgia Institute of Technologypeople.math.gatech.edu/~etnyre/TechTopology/2014/Dun...tetrahedra! 500 0 500 1000 1500 2000 2500 volume! 500 0 500 1000 1500 2000 2500 slope=0.901 intercept=3.229

0

Simpli�ed: 200 7! 156

Page 13: Georgia Institute of Technologypeople.math.gatech.edu/~etnyre/TechTopology/2014/Dun...tetrahedra! 500 0 500 1000 1500 2000 2500 volume! 500 0 500 1000 1500 2000 2500 slope=0.901 intercept=3.229

0

Simpli�ed: 300 7! 229

Page 14: Georgia Institute of Technologypeople.math.gatech.edu/~etnyre/TechTopology/2014/Dun...tetrahedra! 500 0 500 1000 1500 2000 2500 volume! 500 0 500 1000 1500 2000 2500 slope=0.901 intercept=3.229

crossings0 200 400 600 800 1000

hyperbolicvolume

0

500

1000

1500

2000

2500

slope=2.017

intercept=-27.677

r=0.999

Page 15: Georgia Institute of Technologypeople.math.gatech.edu/~etnyre/TechTopology/2014/Dun...tetrahedra! 500 0 500 1000 1500 2000 2500 volume! 500 0 500 1000 1500 2000 2500 slope=0.901 intercept=3.229

tetrahedra-500 0 500 1000 1500 2000 2500

hyperbolicvolume

-500

0

500

1000

1500

2000

2500

slope=0.901

intercept=3.229

r=1.000

Page 16: Georgia Institute of Technologypeople.math.gatech.edu/~etnyre/TechTopology/2014/Dun...tetrahedra! 500 0 500 1000 1500 2000 2500 volume! 500 0 500 1000 1500 2000 2500 slope=0.901 intercept=3.229

0.0 0.2 0.4 0.6 0.8 1.00.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0

150

300

450

600

750

900

1050

Page 17: Georgia Institute of Technologypeople.math.gatech.edu/~etnyre/TechTopology/2014/Dun...tetrahedra! 500 0 500 1000 1500 2000 2500 volume! 500 0 500 1000 1500 2000 2500 slope=0.901 intercept=3.229

crossings101 102 103 104

volumetim

e

10-3

10-2

10-1

100

101

102

slope=2.601

intercept=-6.827

r=0.957

Page 18: Georgia Institute of Technologypeople.math.gatech.edu/~etnyre/TechTopology/2014/Dun...tetrahedra! 500 0 500 1000 1500 2000 2500 volume! 500 0 500 1000 1500 2000 2500 slope=0.901 intercept=3.229

crossings-200 0 200 400 600 800 1000 1200

bridge

number

-50

0

50

100

150

200

slope=0.145

intercept=2.417

r=0.995

Page 19: Georgia Institute of Technologypeople.math.gatech.edu/~etnyre/TechTopology/2014/Dun...tetrahedra! 500 0 500 1000 1500 2000 2500 volume! 500 0 500 1000 1500 2000 2500 slope=0.901 intercept=3.229

crossings-100 0 100 200 300 400 500 600 700 800

genu

s

-50

0

50

100

150

200

Page 20: Georgia Institute of Technologypeople.math.gatech.edu/~etnyre/TechTopology/2014/Dun...tetrahedra! 500 0 500 1000 1500 2000 2500 volume! 500 0 500 1000 1500 2000 2500 slope=0.901 intercept=3.229

crossings0 100 200 300 400 500 600

Chern-Simon

s

-0.2

-0.1

0.0

0.1

0.20.2

Page 21: Georgia Institute of Technologypeople.math.gatech.edu/~etnyre/TechTopology/2014/Dun...tetrahedra! 500 0 500 1000 1500 2000 2500 volume! 500 0 500 1000 1500 2000 2500 slope=0.901 intercept=3.229
Page 22: Georgia Institute of Technologypeople.math.gatech.edu/~etnyre/TechTopology/2014/Dun...tetrahedra! 500 0 500 1000 1500 2000 2500 volume! 500 0 500 1000 1500 2000 2500 slope=0.901 intercept=3.229
Page 23: Georgia Institute of Technologypeople.math.gatech.edu/~etnyre/TechTopology/2014/Dun...tetrahedra! 500 0 500 1000 1500 2000 2500 volume! 500 0 500 1000 1500 2000 2500 slope=0.901 intercept=3.229

crossings

101 102 103

bridge

numbertime

10-1

100

101

102

103

104

slope=2.000

intercept=-3.897

r=0.845


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