Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Forgot your password?
• Apply for membership

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeMay 30th 2013
   • PermaLink
   Author: Urs
   Format: MarkdownItexI am starting an entry _[[Poincaré duality algebra]]_, but it still needs some attention

   I am starting an entry Poincaré duality algebra, but it still needs some attention

2. • CommentRowNumber2.
   • CommentAuthorjim_stasheff
   • CommentTimeMay 30th 2013
   • PermaLink
   Author: jim_stasheff
   Format: TextWhy start with C^* algebras surely there are many other Poincaré duality algebras jim

   Why start with C^* algebras
   surely there are many other Poincaré duality algebras
   
   jim
3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeMay 30th 2013
   • PermaLink
   Author: Urs
   Format: MarkdownItexokay, I have added the definition _[For graded-commutative algebras](http://ncatlab.org/nlab/show/Poincar%C3%A9+duality+algebra#ForGradedCommutativeAlgebras)_. Let me know your favorite reference, and I'll add it, too.

   okay, I have added the definition For graded-commutative algebras.

   Let me know your favorite reference, and I’ll add it, too.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJul 7th 2013
   • (edited Jul 7th 2013)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded to _[[Poincare duality algebra]]_ * two more references on the $C^\ast$-case; * remarks highlighting that the $C^\ast$-case is about duality in K-theory as opposed to in ordinary cohomology; * a remark that for [[twisted groupoid convolution algebras]] the fact that the Poincaré duality is to the _opposite_ algebra corresponds to keeping the same groupoid (up to equivalence) but inverting the twist (this is no hard to see, but if anyone knows a place where this is remarked in the literature, I'd be grateful for a pointer.)

   added to Poincare duality algebra

   • two more references on the $C^\ast$-case;

   • remarks highlighting that the $C^\ast$-case is about duality in K-theory as opposed to in ordinary cohomology;

   • a remark that for twisted groupoid convolution algebras the fact that the Poincaré duality is to the opposite algebra corresponds to keeping the same groupoid (up to equivalence) but inverting the twist

     (this is no hard to see, but if anyone knows a place where this is remarked in the literature, I’d be grateful for a pointer.)

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeJul 8th 2013
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added at _[K-orientation and Umkehr maps](http://ncatlab.org/nlab/show/Poincar%C3%A9+duality+algebra#PropertiesKOrientationAndUmkehrMaps)_ discussion of push-forward in twisted K-theory. Essentially the same discussion I have (with slight editorial changes) also copied to * _[Freed-Witten-Kapustin anomaly cancellation -- Details](http://ncatlab.org/nlab/show/Freed-Witten+anomaly#Details)_ * _[Push-forward in generalized cohomology -- In twisted K theory](http://ncatlab.org/nlab/show/fiber+integration#KKPushforwardAlongGeneralMap)_. Also added more related references to all these entries.

   I have added at K-orientation and Umkehr maps discussion of push-forward in twisted K-theory.

   Essentially the same discussion I have (with slight editorial changes) also copied to

   • Freed-Witten-Kapustin anomaly cancellation – Details

   • Push-forward in generalized cohomology – In twisted K theory.

   Also added more related references to all these entries.

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeJul 16th 2013
   • PermaLink
   Author: Urs
   Format: MarkdownItexrelated discussion on MO [here](http://mathoverflow.net/a/136908/381)

   related discussion on MO here