Homology, Homotopy and Applications
Volume 15 (2013)
Simplicial polytope complexes and deloopings of $K$-theory
Pages: 301 – 330
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.
Waldhausen $K$-theory, scissors congruence
2010 Mathematics Subject Classification
13D15, 18D05, 18F25, 19D99