The fibre of an iterative adjunction of cells

✍ Scribed by Yves Félix

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 754 KB
• Volume: 119
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(96)00018-7

✦ Synopsis

Let (Y,,%') be a relative CW complex with X and Y simply-connected and suppose that the relative homology H,(Y,X;k) is nonzero. Denote by F the homotopy fibre of the inclusion X -Y. We show that the grade of H,(F;k) as a module over H,(SZY;k) is less than the relative cone length cl( Y,X). This result appears as a corollary of a deeper result concerning differential modules over differential graded algebras. @ 1997 Elsevier Science B.V.