Some Noncommutative Constructions and Their Associated NCCW Complexes

TL;DR

This paper introduces noncommutative topological objects like NC mapping cones and cylinders, explores their NCCW complex structures, and studies their K-theoretic properties and exact sequences.

Contribution

It generalizes noncommutative constructions by defining NC mapping telescopes and analyzes their K-theory and NCCW complex structures.

Findings

Established NCCW complex structures for new noncommutative objects.

Derived K0 and K1 group results for these objects.

Proved cyclic six-term exact sequence theorems for their K-groups.

Abstract

In this article some noncommutative topological objects such as NC mapping cone and NC mapping cylinder are introduced. We will see that these objects are equipped with the NCCW complex structure of [PEDERSEN]. As a generalization we introduce the notions of NC mapping cylindrical and conical telescope. Their relations with NC mappings cone and cylinder are studied. Some results on their K0 and K1 groups are obtained and the cyclic six term exact sequence theorem for their k-groups are proved. Finally we explain their NCCW coplex structure and the conditions in which these objects admit NCCW complex structures.