Lê Modules and Traces

2004/10/11 by David B. Massey, Massey, David B.
Mathematics · #32B10 #32B15 #32C18 #32C35 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:32B10 #msc:32B15 #msc:32C18 #msc:32C35

paper · pdf · doi:10.48550/arxiv.math/0410258

12 pages, to appear in Proc. AMS

arxiv created 2005/02/13 · arxiv updated 2009/12/01

Abstract

We show how some of our recent results clarify the relationship between the Lê numbers and the cohomology of the Milnor fiber of a non-isolated hypersurface singularity. The Lê numbers are actually the ranks of the free Abelian groups -- the Lê modules -- appearing in a complex whose cohomology is that of the Milnor fiber. Moreover, the Milnor monodromy acts on the Lê module complex, and we describe the traces of these monodromy actions in terms of the topology of the critical locus.

Related

• Lê cycles and Milnor classes
• Non-isolated Hypersurface Singularities and Lê Cycles
• Hypersurface Singularities and Milnor Equisingularity
• Milnor monodromies and mixed Hodge structures for non-isolated hypersurface singularities
• Singular cohomology of the analytic Milnor fiber, and mixed Hodge structure on the nearby cohomology