Abstract
Let E(X) be the set of based homotopy classes of based self-homotopy equivalences of a CW-complex X. The concept of E(X) is applied to the category of pairs and is extended to a general concept E(α) for a map α:A→B. In this study, E(α) is generalized to Eγ(α) for two objects α and γ. Several generalized subgroups of E(α) or Eγ(α) are obtained and are combined to form an exact sequence. The exactness and the split property of this sequence is investigated. In particular, the sequence of a product space or a wedge space is demonstrated to be a split exact sequence. The split property and the exactness are used to completely compute those subgroups.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
