Timeline for Does the signature admit a homotopy coherent refinement?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 9, 2013 at 19:29 | vote | accept | Ben Knudsen | ||
| Nov 9, 2013 at 18:56 | answer | added | Ricardo Andrade | timeline score: 7 | |
| Nov 9, 2013 at 18:16 | comment | added | Ben Knudsen | That sounds like a good idea to me. | |
| Nov 9, 2013 at 17:37 | comment | added | Ricardo Andrade | Dear @Ben Knudsen: I am happy my comment helped. Do you think I should copy it to an answer? That would remove this question from the list of unanswered questions. | |
| Nov 9, 2013 at 17:21 | comment | added | Ben Knudsen | @Ricardo: I think your comment answers the question. Thanks! | |
| May 20, 2013 at 20:08 | comment | added | Ben Wieland | Neil: yes, $L$ is well-understood, but you have it backwards: actually, $L[1/2]=KO[1/2]$; $L_{(2)}$ is EM. A simple check: $L$ is 4-periodic, while $KO_{(2)}$ is only 8-periodic. | |
| May 19, 2013 at 17:11 | comment | added | Neil Strickland | @Dylan: if I remember rightly, $L[1/2]$ is equivalent to an Eilenberg-MacLane spectrum, whereas $L_{(2)}$ is equivalent to $kO_{(2)}$, so the $K(n)$-localizations are not hard. However, these are not $E_\infty$ equivalences (or at least not obviously so). | |
| May 18, 2013 at 2:52 | comment | added | Ricardo Andrade | I am unfamiliar with L-theory. Nevertheless, I came across a recent article on the arxiv which seems related: "Commutativity properties of Quinn spectra" (arxiv.org/abs/1304.4759). It states in remark 1.4 that the Sullivan-Ranicki orientation from $MSTop$ to L-theory is a ring map of symmetric ring spectra, which I assume to mean a map of associative/$A_\infty$ monoids. Immediately before that remark, it is also stated that the authors are unaware of any previous result on the multiplicativity of the symmetric signature. Perhaps this article and the references therein will be helpful. | |
| May 17, 2013 at 19:17 | comment | added | Dylan Wilson | Welcome to Mathoverflow! I have no idea what the answer to this is, but it seems hard. We'd have to know something about, like... the units of L-theory...For KO and tmf we knew stuff about the K(n)−localizations and used Rezk′s magic juice; do we know anything about the K(n)−localizations of L-theory? This sounds hard. But also like buckets of fun. | |
| May 17, 2013 at 15:41 | history | asked | Ben Knudsen | CC BY-SA 3.0 |