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### Bounds on rho-invariants and simplicial complexity of triangulated manifolds

**Geometry/Topology**

Speaker: | Geunho Lim, UC Santa Barbara |

Location: | 2112 MSB |

Start time: | Tue, Jan 31 2023, 1:10PM |

In this talk, we show the existence of linear bounds on various rho-invariants. In particular, we construct a desired cobordism over a group, whose complexity is linearly bounded by that of its boundary. Employing a combinatorial concept of G-colored polyhedra, we give linear bounds on Atiyah-Singer invariants of PL manifolds. Using relative hyperbolization, we obtain linear bounds on Cheeger-Gromov invariants of PL manifolds endowed with a faithful representation. As applications, we give concrete examples in the complexity theory of high-dimensional (homotopy) lens spaces. This is a joint work with Shmuel Weinberger.