Lecture Notes for Math 541 Spring 2018 - L
^{2}
Invariants
Note: These are my personal lecture notes. They may contain errors. Some of the previous lectures need to be rewritten so that they are more legible. I will add these later.
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Motivation for studying L
^{2}
Invariants
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Hilbert spaces and l
^{2}
G
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Bounded Operators
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The Group von Neumann Algebra
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Ring Properties of the Group von Neumann Algebra
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Example: von Neumann Algebra for Z
^{m}
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Dimensions of arbitrary modules over NG
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Definition of the L^2 Betti numbers
.....
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Definition of Whitehead torsion over general rings