Geometric Aspects of the Heisenberg Group
نویسندگان
چکیده
I provide a background of groups viewed as metric spaces to introduce the notion of asymptotic dimension of a group. I analyze the asymptotic dimension of Z ⊕ Z and the free group on two generators to better understand the concept of asymptotic dimension. The asymptotic dimension of the Heisenberg group, H, asdimH, has been shown to be three using advanced mathematics. I will try to show that asdimH is three and create a cover for H which will confirm the result about the asymptotic dimension. Also, the Cayley graph of H and the algebraic structure of H is analyzed to help understand this group better.
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