Anaya, J., Cano, A., Castañeda-Alvarado, E., Castillo-Rubí, M. (2018). The Second Symmetric Product of Finite Graphs from a Homotopical Viewpoint. Khayyam Journal of Mathematics, 4(1), 13-27. doi: 10.22034/kjm.2017.53432

José G. Anaya; Alfredo Cano; Enrique Castañeda-Alvarado; Marco A. Castillo-Rubí. "The Second Symmetric Product of Finite Graphs from a Homotopical Viewpoint". Khayyam Journal of Mathematics, 4, 1, 2018, 13-27. doi: 10.22034/kjm.2017.53432

Anaya, J., Cano, A., Castañeda-Alvarado, E., Castillo-Rubí, M. (2018). 'The Second Symmetric Product of Finite Graphs from a Homotopical Viewpoint', Khayyam Journal of Mathematics, 4(1), pp. 13-27. doi: 10.22034/kjm.2017.53432

Anaya, J., Cano, A., Castañeda-Alvarado, E., Castillo-Rubí, M. The Second Symmetric Product of Finite Graphs from a Homotopical Viewpoint. Khayyam Journal of Mathematics, 2018; 4(1): 13-27. doi: 10.22034/kjm.2017.53432

The Second Symmetric Product of Finite Graphs from a Homotopical Viewpoint

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

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.