The ghost length and duality on the chain and cochain type levels
Algebraic Topology
2016-01-27 v3 Rings and Algebras
Representation Theory
Abstract
We establish equalities between cochain and chain type levels of maps by making use of exact functors which connect appropriate derived and coderived categories. Relevant conditions for levels of maps to be finite are extracted from the equalities which we call duality on the levels. Moreover, we give a lower bound of the cochain type level of the diagonal map on the classifying space of a Lie group by considering the ghostness of a shriek map which appears in derived string topology. A variant of Koszul duality for a differential graded algebra is also discussed.
Keywords
Cite
@article{arxiv.1108.3890,
title = {The ghost length and duality on the chain and cochain type levels},
author = {Katsuhiko Kuribayashi},
journal= {arXiv preprint arXiv:1108.3890},
year = {2016}
}
Comments
23 pages. This is a new verision of the preprint "Duality on the (co)chain type levels". The title is changed