Cohomology in algebra, geometry, physicsand statistics

Formally integrable complex structures on higher dimensional knot spaces

Speaker’s name:

Domenico Fiorenza

Speaker’s affiliation:

Università di Roma “La Sapienza”

Place:

ZOOM meeting

Date:

Wednesday, 21. October 2020 - 11:30 to 12:30

Abstract:

By the Brown-Gray’s classification, there are four classes of Riemannian manifolds M with parallel r-fold vector cross products: r = 1 and M a Kähler manifold, r = dim M − 1, r = 2 and M a G_2-manifold, r = 3 and M a Spin(7)-manifold. For the first three classes it has been proven by Brylinski, LeBrun, and Verbitsky, via ad hoc arguments for each of these classes, that the higher knot spaces for M carry a natural formally Kähler structure. More recently, Henrich provided a new proof for the r = dim M − 1 case. In a recent work with Hông Vân Lê (arXiv:1912.05175), we show how a variant of Henrich's construction can be used to provide a uniform proof for all four classes. In particular, this provides a proof for the previously unknown case of Spin(7)-manifolds.

ZOOM meeting shall be opened at 11.15 at

https://cesnet.zoom.us/j/99598413922?pwd=c2Y0TENuZHdDQ3hDWEkySFI3YWo3QT09

Meeting ID: 995 9841 3922

Passcode: cartan

and closed at 13.00

ZOOM meeting shall be opened at 11.15 at

https://cesnet.zoom.us/j/99598413922?pwd=c2Y0TENuZHdDQ3hDWEkySFI3YWo3QT09

Meeting ID: 995 9841 3922

Passcode: cartan

and closed at 13.00