Fourth Edition of the International Conference on Research in Applied Mathematics and Computer Science ICRAMCS 2022
 March 24-25-26, 2022
Online and Face-to-Face Conference

ICRAMCS, 4 (2022) | Proceedings ISSN: 2605-7700

Research Communication | Open Access
Volume 2022 | Communication ID 360
On the rank of induced map in homotopy and homology for fibration
Saloua Chouingou, Abdelhadi Zaim
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
January 30, 2022
March 03, 2308
April 15, 2308

Abstract: Let F→X□(→┴f Y) be a fibration of rationally elliptic CW-complexes. Denote by Im ∏_*▒〖(f)=⊕_i Im {∏_i▒〖(f)〗:∏_i▒〖(X)→∏_i▒〖(Y)〗〗} 〗 and m H_* (f)=⊕_i Im {H_i (f):H_i (X)→H_i (Y)}. The topological aspect of this paper is centred around the following question: when rank ∏_*▒〖(f)≤rank〗 H_* (f)?. We prove this question for certain reasonable cases.