Seminar on perverse sheaves and intersection cohomology

Talk 4: Intersection cohomology 1: Definitions and basic examples (Jordan Levin)

Introduce topological pseudomanifolds and give examples [Ban07, Section 4.1.2]. Introduce the intermediate extension functor j!∗ and prove its alternative characterisation by iterated truncations [Dim04, Definition 5.2.6, Proposition 5.2.10], [BBD82, pp. 1.4.22, 1.4.24, 2.1.11]. Define intersection cohomology with respect to a local system L by IC(L) := j!∗L[dim X] and IHk(L) := Hk−dim X(X, IC(L)), see [Ban07, Eq. 4.13] or [Dim04, Defini-tion 5.4.3]. Compute intersection cohomology in the smooth case and in the case of isolated singularities [Dim04, Proposition 5.4.4].