Invariants of continuous fields of C* algebras
Abstract
The goal of this thesis is to describe the equivariant E-theory group for a class of continuous fields of C* algebras over the unit interval [0,1]. As explained in the introduction, this provides us with a way to classify maps between such fields, and to understand them better through K-theoretic models. In Chapter 1, we review the notion of a continuous field of C* algebras, and describe some examples which will be important in subsequent chapters. Chapter 2 reviews the basic object of our investigation — the EX group. We describe asymptotic C 0(X)-homomorphisms, construct the E-theory group, and prove some basic properties of the group. We then show the existence of a short exact sequence for computing the group EX( A,B) where A is a skyscraper algebra. In Chapter 3, we introduce elementary fields over the unit interval. Our main result is an explicit calculation of EX(A,B) for elementary fields A and B over [0,1] which satisfy the condition that E1(D,E) = 0 for any two fibers D, E occurring in either A or B. We use this calculation to show that, if the fibers satisfy the UCT and have torsion-free K0 groups and zero K 1 groups, then EX(A,B) can be realized as morphisms on the K0 pre-sheaf. We end the thesis by explaining the relevance of these results, and also describe some questions that arise from this work.
Degree
Ph.D.
Advisors
Dadarlat, Purdue University.
Subject Area
Mathematics|Theoretical Mathematics
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