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• CommentRowNumber1.
• CommentAuthorTim_Porter
• CommentTimeNov 6th 2010
• (edited Nov 6th 2010)

I have created a stub for primary homotopy operation. At present it just refers to Whitehead products and composition operations and redirects attention to those entries and to Pi-algebras, which will be next on my list to be created. I do not have access to G. W. Whitehead’s book on homotopy theory so have not given a precise definition nor a discussion of what these are, although the entry on $\Pi$-algebras will to some extent cure that. If anyone knows the definition well or has Whitehead’s book, can they provide the details…. otherwise it will remain a stub. :-(

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeNov 6th 2010

Is there a grammar typo in this sentence

The primary homotopy operations encoded via Pi-algebras into an algebraic structure akin to models for a Lawvere theory.

around “encoded”? I am not sure how to parse the sentence.

• CommentRowNumber3.
• CommentAuthorTim_Porter
• CommentTimeNov 6th 2010

Thanks. The last ’d’ slipped in from another thought pattern!

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeNov 6th 2010
• (edited Nov 6th 2010)

I added a bunch of links to Pi algebra and renamed the entry into singular.

The entry breaks off rather abruptly in the middle of a sentence. Is that how you saved it or did we accidentally lose some material?

• CommentRowNumber5.
• CommentAuthorTim_Porter
• CommentTimeNov 6th 2010
• (edited Nov 6th 2010)

I would love to be able to link up the $\Pi$-algebra stuff with the infinity-groupoid idea, fairly directly. i.e. the weakness of the infinity groupoid operations should be encoded with primary homotopy operations. Blanc, Johnson and Turner have a nice paper that goes a little way in that direction and the fact that Simona Paoli was working with the three of them more recently may mean that something emerges in that direction.

I see you added a linkage to Steenrod algebra. I was not courageous enough to enter that lions den so had left it out! It should be there however.

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeNov 6th 2010

I see you added a linkage to Steenrod algebra. I was not courageous enough to enter that lions den so had left it out! It should be there however.

Keywords should always be linked, even if the corresponding entry does not exist yet.

For if you put the square brackets then at some point in the future when somebody creates that entry, the link will automatically come into existence.

But you you don’t put the brackets then at some point in the future when someboy creates the entry no-one will remember that it needs to be linked to from here.

• CommentRowNumber7.
• CommentAuthorTim_Porter
• CommentTimeNov 6th 2010

You are right, but the keyword in this case is such a large area (that may need looking at for many different n-POV aspects) that I hesitated!

(Actually the Wikipedia article on the Steenrod algebra is quite readable. I am just allergic to the subject as I was bombarded at all the alg.top. meetings I went to as a student. I preferred the topics in the category theory meetings!)