Simplicial Polytope Complexes and Deloopings of $K$-theory

Details Simplicial Polytope Complexes and Deloopings of $K$-theory Simplicial Polytope Complexes and Deloopings of $K$-theory

2011-02-21

arxiv.org/abs/1102.4278v1

Mathematics

Algebraic Topology

Scientific paper

This paper is a continuation of our previous work 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.

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