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Tyler Lawson
Gamma Spaces
Abstract:
The category of $\Gamma$-spaces is a symmetric monoidal category used as a
model for connective spectra. A $\Gamma$-space is a functor from the
category of finite pointed sets to the category of pointed spaces which
preserves the initial object. Many machines for constructing infinite loop
spaces naturally take values in $\Gamma$-spaces, including those associated
to topological abelian monoids, spaces with partially defined
multiplication, modules over an $E_\infty$ operad, and various definitions
of $K$-theory.
We will go over the definitions, compare with other categories of spectra,
construct the symmetric spectrum associated to a $\Gamma$-space, define the
smash product of Lyadakis, and see some examples. Additionally, I will
discuss a generalization to a $G$-equivariant context, where $G$ is a
compact Lie group.
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