On Exact Sequences of the Rigid Fibrations

TL;DR

This paper explores the properties of rigid fibrations, establishing a relationship with topological spaces and homotopy groups, and presents new results in the theory of rigid covering fibrations.

Contribution

It introduces a relation between topological spaces and rigid fibrations, leading to a commutative diagram of homotopy groups and new insights in the field.

Findings

Established a relation between topological spaces and rigid fibrations

Derived a commutative diagram of homotopy groups

Deduced new results in the theory of rigid fibrations

Abstract

In 2002, Biss investigated on a kind of fibration which is called rigid covering fibration (we rename it by rigid fibration) with properties similar to covering spaces. In this paper, we obtain a relation between arbitrary topological spaces and its rigid fibrations. Using this relation we obtain a commutative diagram of homotopy groups and quasitopological homotopy groups and deduce some results in this field.