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SUMMARY:Hood Chatham (MIT)
DTSTART:20200406T203000Z
DTEND:20200406T213000Z
DTSTAMP:20260423T004658Z
UID:MITTop/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITTop/1/">A
 n orientation map for height $p−1$ real $E$ theory</a>\nby Hood Chatham 
 (MIT) as part of MIT topology seminar\n\n\nAbstract\nLet $p$ be an odd pri
 me and let $\\operatorname{EO}=E^{hC_p}_{p−1}$ be the $C_p$ fixed points
  of height $p−1$ Morava $E$ theory. We say that a spectrum $X$ has algeb
 raic $\\operatorname{EO}$ theory if the splitting of $K_*(X)$ as an $K_*[C
 _p]$ module lifts to a topological splitting of $\\operatorname{EO} \\wedg
 e X$. We develop criteria to show that a spectrum has algebraic $\\operato
 rname{EO}$ theory\, in particular showing that any connnective spectrum wi
 th mod $p$ homology concentrated in degrees $2k(p−1)$ has algebraic $\\o
 peratorname{EO}$ theory. As an application\, we answer a question posed by
  Hovey and Ravenel by producing a unital orientation $MW_{4p−4} \\to \\o
 peratorname{EO}$ analogous to the $MSU$ orientation of $KO$ at $p=2$ where
  $MW_{4p−4}$ is the Thom spectrum of the $(4p−4)$-connective Wilson sp
 ace.\n
LOCATION:https://researchseminars.org/talk/MITTop/1/
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