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Research Paper | Mathematics | India | Volume 12 Issue 8, August 2023 | Popularity: 6 / 10

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Exploring Normal Covering Spaces: A Bridge between Algebraic Topology and Abstract Algebra

Dr. Kumari Sreeja S Nair

Abstract: The aim of this study was to introduce normal covering spaces which are a special class of covering spaces. The theory of covering spaces is a relevant topic of Algebraic Topology. Here we give description about the certain properties of the normal covering spaces. A normal covering space is characterised by its isotropy subgroup which is a normal subgroup of the concerned covering space. The study of covering space is closely connected with that of Fundamental group. The detailed explanation of covering spaces is given in [3] & [12]. The structure of Fundamental Group is given in [2], [5], & [11]. The basic results of Abstract Algebra is obtained from [9], & [10]. Normal covering spaces are a class of covering spaces which play a vital role in the study of Algebraic Topology. Here we make use of the algebraic structure used in Abstract Algebra and applied it in Algebraic Topology. The study of this article will help the researchers to do collaborative research with other areas of Mathematics.

Keywords: Fundamental group, covering spaces, fibre set, loop product, homotopy, isotropy subgroup, orbit, stabilizer

Edition: Volume 12 Issue 8, August 2023

Pages: 2474 - 2477

DOI: https://www.doi.org/10.21275/SR23824225856

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