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Contact forms
Contact structures
Contact structures
Contact topology
Contact topology
Fundamental dichotomy:
Tight versus overtwisted
Overtwisted disk
Fundamental dichotomy is a tautology
Fundamental dichotomy is a tautology
overtwisted
tight overtwisted
Classification of overtwisted
contact structures
Classification of overtwisted
contact structures
Classification of tight contact
structures?
Dichotomy between
universally tight
and
virtually overtwisted
(tight) contact structures
The dichotomy between universally tight and
virtually overtwisted contact structures
The dichotomy between universally tight and
virtually overtwisted contact structures
The dichotomy between universally tight and
virtually overtwisted contact structures
Contact structures
tight overtwisted
universally tight virtually overtwisted
MILNOR FILLABLE CONTACT
STRUCTURES
Complex surface singularities
The link of a singularity
The link of a singularity
The link of a singularity
An example of a link of a singularity
Canonical contact structure
Canonical contact structure
Milnor fillable
Topological characterization
Our main result
Our main result
Our main result
What was known?
What was known?
Milnor fillable universally tight
Stein fillable
strongly symplectically fillable
weakly symplectically fillable
tight
There are no other implications!
Proof of the corollary
Proof of the corollary
Proof of the corollary
Proof of the corollary
Proof of the corollary
Proof of the corollary
Proof of the corollary
Proof of the corollary
Proof of the corollary
Outline of the proof:
Outline of the proof:
Outline of the proof:
Another approach ?
