June 2023 On the (n,m)-fold symmetric product suspensions of a finite graph
José G. Anaya, Alfredo Cano, Enrique Castañeda-Alvarado, Marco A. Castillo-Rubí
Adv. Studies: Euro-Tbilisi Math. J. 16(2): 29-46 (June 2023). DOI: 10.32513/asetmj/193220082315


Let X be a continuum and n, Fn(X) denotes the hyperspace of all subsets of X with at most n points. Given m,n with m<n, we consider SFmn(X) as the quotient space Fn(X)/Fm(X). In this paper we will show that SFmn() is a homotopic functor. Thus we will obtain a classification by homotopy. We will study the homotopy type of SF12(X) and we will calculate the Euler characteristic of SFmn(X), when X is a finite graph. Finally, we define a polynomial associated with a finite graph to give particular solutions to the problem: Given m,n, with m<n, if X a continuum such that SFmn(X) is homeomorphic to Fn(X), is X contractible?


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José G. Anaya. Alfredo Cano. Enrique Castañeda-Alvarado. Marco A. Castillo-Rubí. "On the (n,m)-fold symmetric product suspensions of a finite graph." Adv. Studies: Euro-Tbilisi Math. J. 16 (2) 29 - 46, June 2023. https://doi.org/10.32513/asetmj/193220082315


Received: 9 June 2020; Accepted: 7 April 2023; Published: June 2023
First available in Project Euclid: 28 June 2023

MathSciNet: MR4609025
Digital Object Identifier: 10.32513/asetmj/193220082315

Primary: 54B20
Secondary: 54F15 , 55P65 , 55Q52

Keywords: Euler characteristic , finite graph , homotopy functors , hyperspace suspension , Symmetric product

Rights: Copyright © 2023 Tbilisi Centre for Mathematical Sciences


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Vol.16 • No. 2 • June 2023
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