Geodesic
Simplicial polytope complexes and deloopings of $K$-theory
Homology, homotopy, and applications, Tome 15 (2013) no. 2, pp. 301-330.

Voir la notice de l'article provenant de la source International Press of Boston

This paper is a continuation of the author’s previous paper on scissors congruence, in which we defined the notion of a polytope complex and its $K$-theory. In this paper we produce formulas for the delooping of a simplicial polytope complex and the cofiber of a morphism of simplicial polytope complexes. Along the way we also prove that the (classical and higher) scissors congruence groups of polytopes in a homogeneous $n$-manifold (with sufficient geometric data) are determined by its local properties.
DOI : 10.4310/HHA.2013.v15.n2.a18
Classification : 13D15, 18D05, 18F25, 19D99
Keywords: Waldhausen $K$-theory, scissors congruence 
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Inna Zakharevich. Simplicial polytope complexes and deloopings of $K$-theory. Homology, homotopy, and applications, Tome 15 (2013) no. 2, pp. 301-330. doi : 10.4310/HHA.2013.v15.n2.a18. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2013.v15.n2.a18/

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