单纯多胞形复形与$K$理论的去环
Simplicial Polytope Complexes and Deloopings of $K$-theory
摘要：
本文是我们以前工作的继续，我们定义了多胞形复形的概念及其$K$ -理论。本文给出了单纯多胞形复形的去环公式和单纯多胞形复形的态射的上纤维公式。一路上，我们还证明了（经典的和更高的）剪刀同余群的多面体在一个齐次$n$ -流形（有足够的几何数据）是由它的局部性质。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
