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• CommentRowNumber1.
• CommentAuthordomenico_fiorenza
• CommentTimeJun 15th 2010
• (edited Jun 15th 2010)

continued from here

my proposal:

Connes fusion is used to define fusion of positive energy representations of the loop group $\mathcal{L}SU(N)$ in * Antony Wassermann, Operator algebras and conformal field theory III (arXiv) and to define elliptic cohomology in * Stephan Stolz and Peter Teichner, What is an elliptic object? (link)

and removing the query box.

• CommentRowNumber2.
• CommentAuthorzskoda
• CommentTimeJun 15th 2010

You can have a new section Applications and then putting what you wrote, and others can add other similar applications (there are more in my vague memory). I agree.

1. good idea! I’m going to do that :)

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeJun 15th 2010
• (edited Jun 15th 2010)

I edited Connes fusion a little. In particular I rephrased the bit where it said that Stolz-Teichner used Connes fusion to “define elliptic cohomology”. That’s a bit too strong.

What they actually did with this was to sketch a definition of what a connection on a String-principal bundle should be. There was and still is the hope that connections on String-principal bundles relate to elliptic cohomology/tmf as Spin bundles with connection relate to K-theory, but this is far from being solved. Still.

2. I agree.