Monday, December 10, 2007

Saturday, November 17, 2007

Contact structures: dz+xdy-ydx

Contact structure dz+xdy-ydx v4

Contact structure dz+xdy-ydx v3

Some views of the planes in the kernel of the 1-form dz+xdy-ydx

Cosmetic surgery on the Figure Eight Sister

The double branched cover of the closure of the braid on the left is the lens space L(5,1). The braid axis lifts to the Figure Eight Sister. Adding in two full twists downstairs is equivalent to doing +1 surgery on the knot up stairs. After braid moves, we obtain the mirror.

Hence the figure eight sister exterior has two fillings yielding homeomorphic lens spaces.

Scharlemann cycles






















longmobius34

extschcycle34

longmobius25

extschcycle25

longmobius16

extschcycle16

longmobius7t

extschcycle7t

Connect sum







ConnectSum2U

ConnectSum2T








ConnectSum0U

ConnectSum0T








ConnectSum1U

ConnectSum1T

Blackboard pictures

Photo 5

Photo 6

Photo 8

Photo 7

Grid diagram and trefoil











Grid Trefoil

Grid Trefoil Tetra

Grid Trefoil Torus

Grid Trefoil Tetra Torus











Side Trefoil

Side Trefoil Tetra

Side Trefoil Torus

Side Trefoil Tetra Torus

Twisted Saddles

Figure Eight and Braid


Hmmm.... I'll have to figure out how to put these in the correct order.

Contact structure


ctctstr4, originally uploaded by epsilon_is_afraid_of_zeta.


ctctstr2
ctctstr3


Here we see one view of some 2-planes of the standard contact structure.