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G. Olav Helle 3-31-2022

Title:  Calculations of equivariant instanton Floer groups for binary polyhedral spaces.
Abstract:  Binary polyhedral spaces are the quotient manifolds obtained
from the canonical action of the finite subgroups of SU(2) on the
3-sphere. In this talk I will discuss calculations of the equivariant
instanton Floer groups, in the sense of Miller Eismeier, for the
trivial SU(2)-bundle over this family of manifolds.
Due to work of Austin and Kronheimer one may obtain very precise
information about the instanton moduli spaces over the cylinders
associated with these manifolds. If one requires 2 to be invertible
in the ring of coefficients, this is sufficient to explicitly identify
the complexes calculating equivariant instanton Floer homology. From
there it is a matter of algebra to extract explicit calculations
in all cases.
Notes

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