Geometry and Topology Seminar —— Immersions of Punctured 4-manifolds: with Applications to Quantum Cellular Automata
报告人：Matthias Kreck (University of Bonn)
时间：2026-03-04 15:10-17:00
地点：智华楼四元厅（225）
【摘要】
I will report about a recent paper with Michael Freedman, Daniel Kasprowski, Peter Teichner with an appendix by Alan W. Reid. We study a partial order of closed, connected and smooth n-dimensional manifolds, which simply says that M ≤ N, if there is an immersion of M - pt into N. This is motivated by a result concerning quantum cellular automata on smooth n-manifolds which says that quantum cellular automata are pulled back by immersions. That said I will not say a single word about quantum cellular automata, simply because I know verbally nothing about them. Instead I refer to an appendix in our paper by Mike Freedman. For me this partial order is just a more or less natural relation on smooth manifolds and my motivation was to take part in a first attempt to say something non trivial. In dimension ≤ 3 one has a rather complete picture but in dimension 4 it turns out to be rather interesting and rich. I will report about the results in dim ≤ 3 and outline some main results and techniques in dim 4.
