Hudson, Daniel2019-05-022019-05-0220192019-05-02http://hdl.handle.net/1828/10837The goal of this thesis is to give an introduction to the geometric picture of bivariant K-theory developed by Emerson and Meyer building on the ideas Connes and Skandalis, and then to apply this machinery to give a geometric proof of a result of Emerson. We begin by giving an overview of topological K-theory, necessary for developing bivariant K-theory. Then we discuss Kasparov's analytic bivariant K-theory, and from there develop topological bivariant K-theory. In the final chapter we state and prove the result of Emerson.enAvailable to the World Wide WebK-TheoryAlgebraic TopologyKK-TheoryOperator AlgebrasNon-Commutative GeometryThesis