For more information about this meeting, contact Ping Xu, Nigel Higson, Mathieu Stienon.
| Title: | A Lefschetz number theorem for differential operators |
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| Seminar: | GAP Seminar |
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| Speaker: | Ajay Ramadoss, Cornell University |
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| Abstract: |
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| Let $X$ be a compact, complex manifold and let $E$ be a holomorphic vector bundle on $X$. Let $ Diff^{\bullet}(E)$ be the Dolbeault resolution of the sheaf of holomorphic differential operators on $E$. A construction due to Feigin, et. al , gives a linear functional on the $0$-th Hochschild homology of $Diff^{\bullet}(E)$. This functional "extends" to a linear functional on the "completed" $0$-th Hochschild homology of $Diff^{\bullet}(E)$ ,thereby giving a linear functional $I_E$ on the top cohomology $\text{H}^{2n} (X,\mathbb C)$ of $X$ with complex coefficients. The main result is that $I_E$ is just integration over $X$. As a consequence, one obtains a Lefschetz number formula for a global holomorphic differential operator on $E$. |
Room Reservation Information
| Room Number: | MB106 |
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| Date: | 12 / 01 / 2009 |
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| Time: | 02:30pm - 03:30pm |
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