Upper and lower bounds of the (co)chain type level of a space
Algebraic Topology
2011-02-17 v3 Rings and Algebras
Representation Theory
Abstract
We establish an upper bound for the cochain type level of the total space of a pull-back fibration. It explains to us why the numerical invariant for a principal bundle over the sphere are less than or equal to two. Moreover computational examples of the levels of path spaces and Borel constructions, including biquotient spaces and Davis-Januszkiewicz spaces, are presented. We also show that the chain type level of the homotopy fibre of a map is greater than the E-category in the sense of Kahl, which is an algebraic approximation of the Lusternik-Schnirelmann category of the map. The inequality fits between the grade and the projective dimension of the cohomology of the homotopy fibre.
Keywords
Cite
@article{arxiv.1006.2669,
title = {Upper and lower bounds of the (co)chain type level of a space},
author = {Katsuhiko Kuribayashi},
journal= {arXiv preprint arXiv:1006.2669},
year = {2011}
}
Comments
22 pages. Minor corrections