Ota, Radheshyam (2009) Kan Extension. PhD thesis.
Under a set of conditions, the Kan extension of an additive homology theory over smaller admissible subcategory is again a homology theory. A homology theory over the category of simply connected based topological spaces and continuous maps arising through Kan extension process, from an additive homology theory over a smaller subcategory always admits global Adams cocompletion. A cohomology theory on the category of spaces whose homotopy groups are in a Serre class of abelian groups, which is moreover an acyclic ideal of abelian groups, extends to a cohomology theory on the category of 1-connected based topological spaces having the homotopy type of a CW-complex; also under more restrictive conditions a cohomology on the latter category and the Kan extension of its restriction to the former category are suitably related.
|Item Type:||Thesis (PhD)|
|Uncontrolled Keywords:||Homology Theory, Serre class of abelian groups, cohomology theory, CW-complex.|
|Subjects:||Mathematics and Statistics > Topology|
|Divisions:||Sciences > Department of Mathematics|
|Deposited By:||Hemanta Biswal|
|Deposited On:||28 Jul 2011 09:28|
|Last Modified:||28 Jul 2011 09:28|
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