Special Issue — Dedicated to the 60th Birthday of Jozef Przytycki, Volume II; Guest Editors: M. K. Dabkowski, V. Harizanov, L. H. Kauffman, J. H. Przytycki, R. Sazdanovic and A. SikoraNo Access

Extended quandle spaces and shadow homotopy invariants of classical links

Seung Yeop Yang

Seung Yeop Yang

Department of Mathematics, The George Washington University, Washington, DC 20052, USA

E-mail Address: syyang@gwu.edu

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https://doi.org/10.1142/S0218216517410103Cited by:3 (Source: Crossref)

Abstract

In 1993, Fenn, Rourke and Sanderson introduced rack spaces and rack homotopy invariants, and modifications to quandle spaces and quandle homotopy invariants were introduced by Nosaka in 2011. In this paper, we define the Cayley-type graph and the extended quandle space of a quandle in analogy to rack and quandle spaces. Moreover, we construct the shadow homotopy invariant of a classical link and prove that the shadow homotopy invariant is equal to the quandle homotopy invariant multiplied by the order of a quandle.

Dedicated to Professor Józef H. Przytycki for his 60th birthday

Keywords:

AMSC: 57M27, 55N35, 55Q52

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