Formality of the constructible derived category for spheres: A combinatorial and a geometric approach
Algebraic Topology
2008-11-04 v1
Abstract
We describe the constructible derived category of sheaves on the -sphere, stratified in a point and its complement, as a dg module category of a formal dg algebra. We prove formality by exploring two different methods: As a combinatorial approach, we reformulate the problem in terms of representations of quivers and prove formality for the 2-sphere, for coefficients in a principal ideal domain. We give a suitable generalization of this formality result for the 2-sphere stratified in several points and their complement. As a geometric approach, we give a description of the underlying dg algebra in terms of differential forms, which allows us to prove formality for -spheres, for real or complex coefficients.
Cite
@article{arxiv.0811.0191,
title = {Formality of the constructible derived category for spheres: A combinatorial and a geometric approach},
author = {Anne Balthasar},
journal= {arXiv preprint arXiv:0811.0191},
year = {2008}
}