We give a survey on the connections between Floer theory, arc spaces and singularities. We will start by defining Floer cohomology groups associated to isolated hypersurface singularities as well as contact loci and give some applications and conjectures. After that we speculate how a similar story can be applied to general isolated singularities. At the end of this survey we will look at quotient singularities and their connection with the cohomological McKay correspondence. Much of this article is speculative.

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Floer Theory, Arc Spaces and Singularities

  • Mark McLean

摘要

We give a survey on the connections between Floer theory, arc spaces and singularities. We will start by defining Floer cohomology groups associated to isolated hypersurface singularities as well as contact loci and give some applications and conjectures. After that we speculate how a similar story can be applied to general isolated singularities. At the end of this survey we will look at quotient singularities and their connection with the cohomological McKay correspondence. Much of this article is speculative.