Homology, Homotopy and Applications

Volume 18 (2016)

Number 2

The ghost length and duality on the chain and cochain type levels

Pages: 107 – 132

DOI: https://dx.doi.org/10.4310/HHA.2016.v18.n2.a6


Katsuhiko Kuribayashi (Department of Mathematical Sciences, Faculty of Science, Shinshu University, Matsumoto, Nagano, Japan)


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.


level, differential graded algebra, triangulated category, Koszul duality

2010 Mathematics Subject Classification

13D07, 16E45, 18E30, 55R20

Published 29 November 2016