JP Journal of Geometry and Topology
Volume 11, Issue 3, Pages 209 - 233
(November 2011)
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MAPPING CONE SEQUENCES AND A GENERALIZED NOTION OF CONE LENGTH
Nicholas A. Scoville
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Abstract: We introduce a weighted length between spaces. This is accomplished by using the numerical invariants of cone length and killing length as a framework and by considering other topological invariants to determine the complexity of spaces. This leads us to the definition of a weighted length between spaces. We estimate the weighted length amongst certain maps and spaces for pushouts, pullbacks, and fibrations. Examples of specific weights are given to show that hypotheses in theorems are necessary. |
Keywords and phrases: Lusternik-Schnirelmann category, mapping cone sequence, cone length, killing length, numerical invariants. |
Communicated by Yasuo Matsushita |
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