The Baum-Connes Conjecture Of Crystallographic Groups

In this paper,we introduce the Baum-Connes conjecture of Crystallographic groups,and calculate the K-homology of 2-dimensional crystallographic groups with a new method.This method only needs considering the fixed points of group actions and related general homology group.It greatly simplifies the calculation of K-homology of the universal spaces of groups,and has a very intuitive geometric interpretation.In addition,the calculation results verify the Baum-Connes conjecture of 2-dimensional crystallographic groups,and provide a new perspective for the accurate description of the assembly map of the Baum-Connes conjecture of crystallographic groups.