The Second Symmetric Product of Finite Graphs from a Homotopical Viewpoint

Document Type : Original Article

Authors

José G. Anaya ¹

Alfredo Cano ²

Enrique Castañeda-Alvarado ¹

Marco A. Castillo-Rubí ¹

¹ Facultad de Ciencias, Universidad Autónoma del Estado de México, Instituto Literario No. 100, Col. Centro, C. P. 50000, Toluca, México.

² Facultad de Ciencias, Universidad Autónoma del Estado de México, Instituto Literario No. 100, Col. Centro, C. P. 50000, Toluca, México.

10.22034/kjm.2017.53432

Abstract

This paper describes the classification of the $n$-fold symmetric product of a finite graph by means of its homotopy type, having as universal models the $n$-fold symmetric product of the wedge of $n$-circles; and introduces a CW-complex called $binomial\ torus$, which is homeomorphic to a space that is a strong deformation retract of the second symmetric products of the wedge of $n$-circles. Applying the above we calculate the fundamental group, Euler characteristic, homology and cohomology groups of the second symmetric product of finite graphs.

Keywords

Hyperspaces

symmetric product

finite graph

homotopy

Subjects

• 54 General topology
• 55 Algebraic topology

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