String topology and homotopy skein modules

I will survey what is known about homotopy skein modules of oriented 3-manifolds. These are skein modules based on the link homotopy relation as introduced by Milnor in 1954. In particular I will discuss natural presentations of the modules and how torsion in the modules is computable from a string topology pairing defined by Chas and Sullivan. The technical tools used are from Vassiliev theory as applied by Kalfagianni and Lin in their construction of finite type invariants. Finally I will discuss the geometric invariants determining the image of a link in the skein module, relating back to Milnor's link group and Koschorke's configuration space invariants.

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