@article{oai:soar-ir.repo.nii.ac.jp:00011754,
 author = {Kuribayashi,  Katsuhiko},
 issue = {4},
 journal = {JOURNAL OF PURE AND APPLIED ALGEBRA},
 month = {Apr},
 note = {The level of a module over a differential graded algebra measures the number of steps required to build the module in an appropriate triangulated category. Based on this notion, we introduce a new homotopy invariant of spaces over a fixed space, called the level of a map. Moreover, we provide a method to compute the invariant for spaces over a K-formal space. This enables us to determine the level of the total space of a bundle over the 4-dimensional sphere with the aid of Auslander-Reiten theory for spaces due to Jorgensen. We also discuss the problem of realizing an indecomposable object in the derived category of the sphere by the singular cochain complex of a space. The Hopf invariant provides a criterion for the realization., Article, JOURNAL OF PURE AND APPLIED ALGEBRA. 216(4):752-765 (2012)},
 pages = {752--765},
 title = {On the levels of maps and topological realization of objects in a triangulated category},
 volume = {216},
 year = {2012}
}