Date | 2023-10-24 |
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Speaker | Geunho Lim |

Dept. | Einstein Institute of Mathematics, Hebrew University of Jerusalem |

Room | 27-116 |

Time | 11:00-12:00 |

Using L^2 cohomology, Cheeger and Gromov define the L^2 rho-invariant on manifolds with arbitrary fundamental groups, as a generalization of the Atiyah-Singer rho-invariant. There are many interesting applications in geometry and topology. In this talk, we show linear bounds on the rho-invariants in terms of simplicial complexity of manifolds. First, we obtain linear bounds on Cheeger-Gromov invariants, using hyperbolizations. Next, we give linear bounds on Atiyah-Singer invariants, employing a combinatorial concept of G-colored polyhedra. As applications, we give new concrete examples in the complexity theory of high-dimensional (homotopy) lens spaces. This is a joint work with Shmuel Weinberger.

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