Deformation of Homotopy into Isotopy in Oriented 3-manifolds
نویسندگان
چکیده
We will show that deformation quantization in skein theory of oriented 3-manifolds is induced from a topological deformation quantization of the fundamental 2-groupoid of the space of immersions of circles in M . The structure of skein module and its relations with string topology homomorphisms appear through representations of the groupoid structure into the set the objects. The deformation of the fundamental 2-groupoid is defined by the singularity stratification, the quantization by passage to isotopy classes. Several explicit properties and computations of skein modules are proved. It will be shown that local systems on the space of immersions are important for the understanding of HOMFLY oriented and framed skein theory. The passage from Conway to Jones skein theory is described on the categorical level.
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