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Toward an algebraic Donaldson-Floer theory (survey). (Chinese. English summary) Zbl 1499.14093

Summary: We survey the author’s recent construction of the relative Donaldson polynomial invariants of pairs of smooth divisors in smooth surfaces, taking values in an operational algebraic Floer homology group. We conjecture that this pair forms an algebraic Donaldson-Floer theory.

MSC:

14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)
57R57 Applications of global analysis to structures on manifolds
57R58 Floer homology
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