Persistence of Topological Properties through Layer Map

Anas E; Baby Chacko

doi:https://doi.org/10.14445/22315373/IJMTT-V59P513

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 59 | Number 2 | Year 2018 | Article Id. IJMTT-V59P513 | DOI : https://doi.org/10.14445/22315373/IJMTT-V59P513

Persistence of Topological Properties through Layer Map

Anas E, Baby Chacko

Abstract

In Topology, two spaces are said to be homeomorphic if there exist a homeomorphism between them. It is difficult to consider all functions from one space to other for verifying they are homeomorphic or not. Triangulation of spaces in to simplicial complex is useful in determining the topological properties of spaces. In this paper Layer Topology and Layer Maps on Simplices are used as the tools to prove the homeomorhism between simplices.

Keywords

Barycentric Map, Layer Topology, Layer Map

References

[1] Anas E and Baby Chacko, Barycentric Map and Layer Topology on Simplices, International Journal of Mathematics Trends and Technology (IJMTT) – Volume X Issue October 2017, 33-35
[2] James R. Munkers, Elements of Algebraic Topology, Addison-Wesley Publishing Company, Menlo Park, California. 1984.
[3] K.D.Joshi. Introduction to General Topology, New Age International (P) Ltd., Publishers. New Delhi: 2006.
[4] J. Munkres, Topology, Prentice-Hall, Inc. Englewood Cliffs, N.J. 1975.
[5] John B Fraleigh, A First Course in Abstract Algebra, Dorling Kindersley(India) Pvt Ltd.,2006
[6] Tamal K Dey, Herbert Edels Brunner,Sumanta Guha and Dmitry V. Nekhayev. “Topology Preserving Edge Contraction”. Publication De L’Institute Mathematique, Nouville serie tome66(80) (1999), 23-45
[7] Herbert Edelsbrunner and Nimish R. Shah. Triangulating Topological Spaces. International Journal of Computational Geometry&Applications.Vol 7,No.4(1997) 365-378
[8] D.Burghelea and T.K.Dey. Topological persistence forcircle valued maps. Discrete Comput. Geom., 50(1)(2013), 69-98
[9] O. Busaryev, S.Cabello, C.Chen, T.K.Dey and Y wang. Annotating simplices with homology basis and its applications. Proc. 13th Scandinavian Sympos. Workshops algorithm Theory(SWAT 2012),(2012), 189-200.
[10] G.Calsson and V. de Silva. Zigzag persistence. Fond. Comput. Math. 10(4), 367-405, 2010.
[11] G.Calsson, V. de Silva and D. Morozov. Zigzag persistent homology and real- valued functions. Proc. 26th Annu. Sympos. Comput. Geom. (2009), 247-256
[12] Richard jerrard. Homology with Multiple-valued Functions Applied to Fixed Points. Transactions of The American Mathematical Society. Vol. 213, 1975.
[13] Allen Hatcher. Algebraic Topology. Cambridge University Press.2002.

Citation :

Anas E, Baby Chacko, "Persistence of Topological Properties through Layer Map," International Journal of Mathematics Trends and Technology (IJMTT), vol. 59, no. 2, pp. 85-87, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V59P513