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Danny Vera
Further into the Darkside: Parameterized Orthogonal Spectra
Abstract:
Monsters called "spectra" come in many varieties and sub-species. In
this talk we will discuss the species known as parameterized orthogonal
$G$-spectra over a fixed base $B$. Intuitively an orthogonal spectrum
over $B$ is a collection of $B$-parameterized spaces $X(\lambda)$ for
each $G$-representation $\lambda$ and structure maps $\sigma :
X(\lambda) \smash_{B} S^{\lambda '} \to X(\lambda \oplus \lambda ')$.
We will first look at two different categories of parameterized
$G$-spaces for a compact Lie group $G$ and discuss what it means for a
category to be topologically bicomplete. Together these two categories
of parameterized $G$-spaces form a structure called a $G$-category and
have several layers of enrichment. We will then define parameterized
orthogonal $G$-spectra and if time permits discuss the change of base
functors that allow us to go between the parameterized and
non-parameterized worlds.
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