Intersection cohomology of S¹ symplectic quotients and small resolutions

1998/10/07 by Eugene Lerman, Lerman, Eugene, Susan Tolman +1
Mathematics · #58F05 (Primary) 32C42 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.AG #math.AT #math.DG #math.SG #msc:32C42 #msc:58F05

paper · pdf · doi:10.48550/arxiv.math/9810046

17 pages, LaTeX 2e

arxiv created 1998/10/07 · arxiv updated 2009/11/30

Abstract

We provided two explicit formulas for the intersection cohomology (as a graded vector space with pairing) of the symplectic quotient by a circle in terms of the S¹ equivariant cohomology of the original symplectic manifold and the fixed point data. The key idea is the construction of a small resolution of the symplectic quotient.

Related

• The cosupport axiom, equivariant cohomology and the intersection cohomology of certain symplectic quotients
• Intersection cohomology and quantum cohomology of conical symplectic resolutions
• Intersection cohomology of representation spaces of surface groups
• Cohomology pairings on singular quotients in geometric invariant theory
• Intersection Cohomology of Symplectic Quotients