On Algebraic and Topological Properties of Some Fundamental Groups
Article Sidebar
Main Article Content
Abstract
In this paper, we study the algebraic and topological properties of some topological spaces. We note that the fundamental group of a topological group is abelian and we study some spaces of the same homotopy type with the unit circle S1 . The basic group of the unit circle S1 is isomorphic to the additive group of integers. We say that a topological space is simply connected if it is path-connected and has a trivial fundamental group. We show that the fundamental group of a n-punctured plane is free and we characterize some surfaces as topologically distinct.
Downloads
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
How to Cite
References
C. Godbillon, Élément de topologie algébrique, Hermann Paris, (1971). DOI: https://doi.org/10.5802/aif.1283.
James R. Munkres, James W Munkres. Elements of Algebraic Topology, Taylor & Francis Group, 17 juin 2019. DOI: https://doi.org/10.1201/9780429493911.
Latch, D.M., Thomason, R.W. & Wilson, W.S. Simplicial Sets from categories. Maths Z 164, 195-214 (1979). Doi : https://doi.org/10.1007/BF01182267.
Allen Hatcher. Algebraic topology. Cambridge University Press, Cambridge, 2002. DOI: https://doi.org/10.1017/S0013091503214620.
John M. Lee. Homotopie et groupe fondamental; Graduate Texts in Mathematics, volume 202. Springer, New York, 2011
https://perso.math.u-pem.fr/fradelizi.matthieu/pdf/tpe-lecomte-13.pdf
Kanev, V. Elon Lages Lima. Fundamental groups and Covering spaces. Rend. Circ. Mat. Palermo 52, 510 (2003). DOI: https//doi.org/101007/BF02872769.
G. W. Whitehead. Eléments de la théorie de l’homotopie, Département de Mathématiques, Massachusetts Institute of Technology, Cambridge, Etats-Unis. Graduate Texts in Mathematics (GTM, volume 61), 29 mai 2017. Springer New York. DOI. : https://doi.org/10.1007/978-1-4612-6318-0.
Yves Félix Daniel Tanré, Topologie Algébrique, cours et exercices résolus, DUNOD 2010. DOI : https://doi.org/10.1007/978-981-13-1534-3.
Prasanna, A., kumar, M. P., Mohideen, S. I., & Gulzar, Muhammad. (2020). Algebraic Properties on Fuzzy Translation and Multiplication in BP– Algebras. In International Journal of Innovative Technology and Exploring Engineering (Vol. 9, Issue 3, pp. 123–126). https://doi.org/10.35940/ijitee.b6277.019320
Selvarathi, M. (2019). Algebraic Properties of Implication-Based Anti-Fuzzy Subgroup over a Finite Group. In International Journal of Engineering and Advanced Technology (Vol. 9, Issue 1s4, pp. 1116–1120). https://doi.org/10.35940/ijeat.a1208.1291s419
Mankena, R., Kumar, T. V. P., Ramprasad, Ch., & Kumar, J. V. (2019). Algebraic Structures of m-polar Fuzzy Matrices. In International Journal of Recent Technology and Engineering (IJRTE) (Vol. 8, Issue 3, pp. 3025–3033). https://doi.org/10.35940/ijrte.c4855.098319
Bashir, S. (2023). Pedagogy of Mathematics. In International Journal of Basic Sciences and Applied Computing (Vol. 10, Issue 2, pp. 1–8). https://doi.org/10.35940/ijbsac.b1159.1010223