Relative Homotopy in Relational Structures

Witbooi, P. J.

Canadian mathematical bulletin, Tome 51 (2008) no. 2, pp. 310-320

Résumé

The homotopy groups of a finite partially ordered set (poset) can be described entirely in the context of posets, as shown in a paper by $\text{B}$ . Larose and $\text{C}$ . Tardif. In this paper we describe the relative version of such a homotopy theory, for pairs $\left( X,\,A \right)$ where $X$ is a poset and $A$ is a subposet of $X$ . We also prove some theorems on the relevant version of the notion of weak homotopy equivalences for maps of pairs of such objects. We work in the category of reflexive binary relational structures which contains the posets as in the work of Larose and Tardif.

Détail

DOI : 10.4153/CMB-2008-031-8

Mots-clés : 55Q05, 54A05, 18B30, binary reflexive relational structure, relative homotopy group, exact sequence, locally finite space, weak homotopy equivalence