2010/06/14 by Katsuhiko Kuribayashi, Kuribayashi, Katsuhiko · 1 citation
Mathematics · #Algebraic Topology (math.AT) #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.AT #math.RA #math.RT
paper · pdf · doi:10.48550/arxiv.1006.2669
22 pages. Minor corrections
arxiv created 2011/02/16 · arxiv updated 2011/02/17
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.