Nilpotent counterexamples to the non-abelian clemens-schmid exact sequence

Abstract

In this paper, we propose an approach to study degeneration of moduli spaces. We introduce a notion of non-abelian Clemens-Schmid exact sequence and use this as a way to study degeneration of moduli spaces of fundamental groups. The main theorem shows that it is impossible to have non-abelian Clemens-Schmid exact sequence in general. The possible modification and possible future study will be discussed. © 2010 Pushpa Publishing House.