On Cup-Products of Cofibers of Maps Between Moore Spaces, Hopf Invariant, and Lusternik-Schnirelmann Category

Author

Marwa A.S. Mosallam, Western Michigan UniversityFollow

Date of Award

8-2021

Degree Name

Master of Arts

Department

Mathematics

First Advisor

Dr. Jeffrey Strom

Second Advisor

Dr.John R. Martino

Third Advisor

Dr. Gene Freudenburg

Fourth Advisor

Dr. Nicholas Scoville

Keywords

CUP-Products, cofibers, Moore Spaces, Hopf invariant, L-S category

Access Setting

Masters Thesis-Open Access

Abstract

In this thesis we make a detailed investigation of the cohomology rings of the cofibers C_β of Moore spaces of dimension 2 by computing the cup products in cofibers and to do so we prove that the Hopf invariant in case of Moore spaces in the zero and nonzero homomorphism case is a homomorphism. We have shown when is 𝓍_r,_k a Co-H-Map. We calculated the homologies and cohomologies of Moore spaces of dimension 2 and of the cofibers C_β where β=𝓍_r,k. We used Lusternik-Schnirelmann category to determine the complexity of C_β.

Recommended Citation

Mosallam, Marwa A.S., "On Cup-Products of Cofibers of Maps Between Moore Spaces, Hopf Invariant, and Lusternik-Schnirelmann Category" (2021). Masters Theses. 5227.
https://scholarworks.wmich.edu/masters_theses/5227