A Morphism of Intersection Homology and Hard Lefschetz
نویسندگان
چکیده
We consider a possibility of the existence of intersection homology morphism, which would be associated to a map of analytic varieties. We assume that the map is an inclusion of codimension one. Then the existence of a morphism follows from Saito’s decomposition theorem. For varieties with conical singularities we show, that the existence of intersection homology morphism is exactly equivalent to the validity of Hard Lefschetz Theorem for links. For varieties with arbitrary analytic singularities we extract a remarkable property, which we call Local Hard Lefschetz.
منابع مشابه
Hard Lefschetz Theorem for Nonrational Polytopes
The Hard Lefschetz theorem is known to hold for the intersection cohomology of the toric variety associated to a rational convex polytope. One can construct the intersection cohomology combinatorially from the polytope, hence it is well defined even for nonrational polytopes when there is no variety associated to it. We prove the Hard Lefschetz theorem for the intersection cohomology of a gener...
متن کاملStratified simplices and intersection homology
Intersection homology is obtained from ordinary homology by imposing conditions on how the embedded simplices meet the strata of a space X . In this way, for the middle perversity, properties such as strong Lefschetz are preserved. This paper defines local-global intersection homology groups, that record global information about the singularities of X . They differ from intersection homology in...
متن کاملIntersection Homology Theory
INTRODUCTION WE DEVELOP here a generalization to singular spaces of the Poincare-Lefschetz theory of intersections of homology cycles on manifolds, as announced in [6]. Poincart, in his 1895 paper which founded modern algebraic topology ([18], p. 218; corrected in [19]), studied the intersection of an i-cycle V and a j-cycle W in a compact oriented n-manifold X, in the case of complementary dim...
متن کاملIntersection homology with general perversities
We study intersection homology with general perversities that assign integers to stratum components with none of the classical constraints of Goresky and MacPherson. We extend Goresky and MacPherson’s axiomatic treatment of Deligne sheaves, and use these to obtain Poincaré and Lefschetz duality results for these general perversities. We also produce versions of both the sheaf-theoretic and the ...
متن کاملLefschetz fibrations, intersection numbers, and representations of the framed braid group
We examine the action of the fundamental group Γ of an mpunctured Riemann surface on the middle dimensional homology of a regular fiber in a Lefschetz fibration, and describe to what extent this action can be recovered from the intersection numbers of vanishing cycles. Basis changes for the vanishing cycles result in a nonlinear action of the framed braid group B̃ on m strings on a suitable spac...
متن کامل