Skip to main content
MathOverflow

Return to Answer

fixed arxiv front-end link, gave title
Source Link
David Roberts ♦
David Roberts ♦
  • 35.4k
  • 11
  • 124
  • 349

Maybe it's wrong of me to add this as a separate answer, but it is a separate thought.

If you read the paper Geordie Williamson and I wrote on the subject, the paper Geordie Williamson and I wrote on the subjectA geometric model for Hochschild homology of Soergel bimodules, you'll see that our theorems identify the Hochschild homology of k[t] with the equivariant cohomology of the circle with a trivial circle action. Thus, the bits in degree 0 and 1 correspond to the cohomology of the circle, and the fact that you get k[t] in each corresponds to the fact that k[t] is the cohomology of the classifying space of the circle as a topological group.

There's actually a generalization of this to all Soergel bimodules (explained in the paper above) which says that the Hochschild homology of any irreducible Soergel bimodule has this form where the cohomology of the circle is replaced by the intersection cohomology of the closure of a Bruhat cell BwB in the corresponding group.

Maybe it's wrong of me to add this as a separate answer, but it is a separate thought.

If you read the paper Geordie Williamson and I wrote on the subject, you'll see that our theorems identify the Hochschild homology of k[t] with the equivariant cohomology of the circle with a trivial circle action. Thus, the bits in degree 0 and 1 correspond to the cohomology of the circle, and the fact that you get k[t] in each corresponds to the fact that k[t] is the cohomology of the classifying space of the circle as a topological group.

There's actually a generalization of this to all Soergel bimodules (explained in the paper above) which says that the Hochschild homology of any irreducible Soergel bimodule has this form where the cohomology of the circle is replaced by the intersection cohomology of the closure of a Bruhat cell BwB in the corresponding group.

Maybe it's wrong of me to add this as a separate answer, but it is a separate thought.

If you read the paper Geordie Williamson and I wrote on the subject, A geometric model for Hochschild homology of Soergel bimodules, you'll see that our theorems identify the Hochschild homology of k[t] with the equivariant cohomology of the circle with a trivial circle action. Thus, the bits in degree 0 and 1 correspond to the cohomology of the circle, and the fact that you get k[t] in each corresponds to the fact that k[t] is the cohomology of the classifying space of the circle as a topological group.

There's actually a generalization of this to all Soergel bimodules (explained in the paper above) which says that the Hochschild homology of any irreducible Soergel bimodule has this form where the cohomology of the circle is replaced by the intersection cohomology of the closure of a Bruhat cell BwB in the corresponding group.

Source Link
Ben Webster ♦
Ben Webster ♦
  • 44.7k
  • 12
  • 126
  • 260

Maybe it's wrong of me to add this as a separate answer, but it is a separate thought.

If you read the paper Geordie Williamson and I wrote on the subject, you'll see that our theorems identify the Hochschild homology of k[t] with the equivariant cohomology of the circle with a trivial circle action. Thus, the bits in degree 0 and 1 correspond to the cohomology of the circle, and the fact that you get k[t] in each corresponds to the fact that k[t] is the cohomology of the classifying space of the circle as a topological group.

There's actually a generalization of this to all Soergel bimodules (explained in the paper above) which says that the Hochschild homology of any irreducible Soergel bimodule has this form where the cohomology of the circle is replaced by the intersection cohomology of the closure of a Bruhat cell BwB in the corresponding group.