Homology, Homotopy and Applications

Volume 9 (2007)

Number 2

Cofibrations in the category of Frölicher spaces: Part I

Pages: 413 – 444

DOI: https://dx.doi.org/10.4310/HHA.2007.v9.n2.a15

Authors

Brett Dugmore (Cadiz Securities, Cape Town, South Africa)

Patrice Pungu Ntumba (Department of Mathematics and Applied Mathematics, University of Pretoria, Hatfield, South Africa)

Abstract

Cofibrations are defined in the category of Fröolicher spaces by weakening the analog of the classical definition to enable smooth homotopy extensions to be more easily constructed, using flattened unit intervals. We later relate smooth cofibrations to smooth neighborhood deformation retracts. The notion of smooth neighborhood deformation retract gives rise to an analogous result that a closed Frölicher subspace $A$ of the Frölicher space $X$ is a smooth neighborhood deformation retract of $X$ if and only if the inclusion $i\colon A\hookrightarrow X$ comes from a certain subclass of cofibrations. As an application we construct the right Puppe sequence.

Keywords

Frölicher space, flattened unit interval, smooth neighborhood deformation retract, smooth cofibration, cofibration with FCIP, Puppe sequence

2010 Mathematics Subject Classification

55P05

Published 1 January 2007