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1. • CommentRowNumber1.
   • CommentAuthorDavid_Corfield
   • CommentTimeDec 23rd 2013
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexHopkins and Lurie's [Ambidexterity in K(n)-Local Stable Homotopy Theory](https://www.math.harvard.edu/~lurie/papers/Ambidexterity.pdf‎) contains things of current interest here. Have we seen that norm map before, relating homotopy coinvariants to invariants in a localised setting?

   Hopkins and Lurie’s Ambidexterity in K(n)-Local Stable Homotopy Theory contains things of current interest here. Have we seen that norm map before, relating homotopy coinvariants to invariants in a localised setting?

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeDec 23rd 2013
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks for the alert! I used to point to the lectures that Jacob Lurie had given about this in Notre Dame and elsewhere, now I have updated these citations with the link to the pdf (in the list of references at _[[motivic quantization]]_ and at _[[motives in physics]]_). I have given this as category:reference-page _[[Ambidexterity in K(n)-Local Stable Homotopy Theory]]_. Notice that in terms of what we have been discussing here recently the article is about un-twisted [[Wirthmüller isomorphisms]] in the interpretation of [[dependent linear type theory]] in [[(infinity,1)-module bundles]] over homotopy types. The un-twisted Wirthmüller morphism is the map "$\mu$" for instance in Construction 4.0.7. In particular the integration map of Construction 4.0.7 is a special case of the integration map in _[[schreiber:Type-semantics for quantization]]_.

   Thanks for the alert!

   I used to point to the lectures that Jacob Lurie had given about this in Notre Dame and elsewhere, now I have updated these citations with the link to the pdf (in the list of references at motivic quantization and at motives in physics).

   I have given this as category:reference-page Ambidexterity in K(n)-Local Stable Homotopy Theory.

   Notice that in terms of what we have been discussing here recently the article is about un-twisted Wirthmüller isomorphisms in the interpretation of dependent linear type theory in (infinity,1)-module bundles over homotopy types. The un-twisted Wirthmüller morphism is the map “$\mu$” for instance in Construction 4.0.7.

   In particular the integration map of Construction 4.0.7 is a special case of the integration map in Type-semantics for quantization (schreiber).

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeDec 23rd 2013
   • (edited Dec 23rd 2013)
   • PermaLink
   Author: Urs
   Format: MarkdownItexAh, and to answer explicitly to your question: > Have we seen that norm map before, yes, that norm map is an untwisted [[Wirthmüller isomorphism]]. To see this compare remark 4.1.12 in [Hopkins-Lurie](http://ncatlab.org/nlab/show/Ambidexterity%20in%20K(n)-Local%20Stable%20Homotopy%20Theory) with (4.7) and the line below (4.8) in [May 05](http://ncatlab.org/nlab/show/Wirthmüller+context#May05).

   Ah, and to answer explicitly to your question:

   Have we seen that norm map before,

   yes, that norm map is an untwisted Wirthmüller isomorphism. To see this compare remark 4.1.12 in Hopkins-Lurie with (4.7) and the line below (4.8) in May 05.

4. • CommentRowNumber4.
   • CommentAuthorDavid_Corfield
   • CommentTimeDec 23rd 2013
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   Author: David_Corfield
   Format: MarkdownItexI thought it felt rather familiar. Also looking at Celiott's [notes](http://www.math.northwestern.edu/~celliott/notre_dame_notes/Lurie_notes.pdf) on Lurie's lectures, I see on p. 19 an analogy between $K(n)$ and primes. Was this what you were thinking of [here](http://nforum.mathforge.org/discussion/5563/taking-the-idea-of-tangent-infinitycategories-seriously/?Focus=44090#Comment_44090), though you said E-theory?

   I thought it felt rather familiar.

   Also looking at Celiott’s notes on Lurie’s lectures, I see on p. 19 an analogy between $K(n)$ and primes. Was this what you were thinking of here, though you said E-theory?

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeDec 23rd 2013
   • (edited Dec 23rd 2013)
   • PermaLink
   Author: Urs
   Format: MarkdownItexAh, yes. I should have said Morava K, not Morava E.

   Ah, yes. I should have said Morava K, not Morava E.