The K-homology of 2-dimensional Crystallographic Groups

TL;DR

This paper computes the topological K-homology of 2D crystal groups using fixed point analysis, confirming the Baum-Connes Conjecture for these groups and providing a simplified computational approach.

Contribution

It introduces a fixed point-based method to compute K-homology of 2D crystal groups, verifying the Baum-Connes Conjecture in this context.

Findings

Confirmed the Baum-Connes Conjecture for 2D crystal groups

Developed a simplified method for K-homology calculation

Provided explicit K-homology computations for these groups

Abstract

In this paper we compute the topological K-homology of 2-dimensional crystal groups. Our method focuses on the fixed point of group action and simplifies the calculation of the K-homology of universal space. The result also verifies the Baum-Connes Conjecture of 2-dimensional crystal groups.