Traces, current algebras, and link homologies
Duration: 1 hour 4 mins
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About this item
| Description: |
Rose, D
Monday 26th June 2017 - 14:30 to 15:30 |
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| Created: | 2017-07-19 17:49 |
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| Collection: | Homology theories in low dimensional topology |
| Publisher: | Isaac Newton Institute |
| Copyright: | Rose, D |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
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| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | We'll show how categorical traces and foam categories can be used to define an invariant of braid conjugacy, which can be viewed as a "universal" type-A braid invariant. Applying various functors, we recover several known link homology theories, both for links in the solid torus, and, more-surprisingly, for links in the 3-sphere. Variations on this theme produce new annular invariants, and, conjecturally, a homology theory for links in the 3-sphere which categorifies the sl(n) link polynomial but is distinct from the Khovanov-Rozansky theory. Lurking in the background of this story is a family of current algebra representations.
This is joint work with Queffelec and Sartori. |
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