K-Homology at Infinity and Higher Index Problems for Metric Spaces

Zheng Luo Тоеў

*(East China Normal University)*

14:00-15:00,April 10,2023 A503

__Abstract:__

We introduce the "CE-by-(H)" coarse fibration structure and the "CEH-by-CEM" group extension structure, respectively, and prove that the coarse Novikov conjecture hold for the discrete space with bounded geometry which admit the "CE-by-(H)" coarse fibration structure and the countable discrete group satisfying the "CEH-by-CEM" group extension structure.
Next we introduce the concept of K-homology at infinity, and establish the index map at infinity, transforming the higher index problem of space into the higher index problem at infinity. As an application, we prove that the coarse Novikov conjecture holds for discrete space with bounded geometry that can be coarsely embedded into an l^p space. These include all box spaces of a residually finite hyperbolic group and a large class of warped cones of a compact space with an action by a hyperbolic group.

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