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.
Anaya, J. G., Cano, A., Castañeda-Alvarado, E., & Castillo-Rubí, M. A. (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
MLA
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
HARVARD
Anaya, J. G., Cano, A., Castañeda-Alvarado, E., Castillo-Rubí, M. A. (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
VANCOUVER
Anaya, J. G., Cano, A., Castañeda-Alvarado, E., Castillo-Rubí, M. A. 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
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