Milnor fibers and Links of Local Complete Intersections

We discuss and prove a number of cohomological results for Milnor fibers, real links, and complex links of local complete intersections with singularities of arbitrary dimension.Comment: 14 page

Notes on Perverse Sheaves and Vanishing Cycles

A working mathematician's summary of many results on the derived category, perverse sheaves, and vanishing cycles. This is the September 2013 version.Comment: 42 page

Critical Points of Functions on Singular Spaces

We compare and contrast various notions of the "critical locus" of a complex analytic function on a singular space. After choosing a topological variant as our primary notion of the critical locus, we justify our choice by generalizing L\^e and Saito's result that constant Milnor number implies that Thom's a_f condition is satisfied.Comment: 35 page