中科院数学与系统科学研究院
数学研究所
学术报告
数理逻辑研讨班
报告人：Aristotelis Panagiotopoulos （Carnegie Mellon University）
题 目：The definable content of homological invariants
时 间：2022.11.11（星期五）10:00-12:00
地 点：腾讯会议: 449-0862-2675
摘 要：In this talk we will develop a framework for enriching various classical invariants of homological algebra and algebraic topology with additional descriptive set-theoretic information. The resulting "definable invariants" can be used for much finer classification than their purely algebraic counterparts. We will illustrate how these ideas apply to the classical Cech cohomology invariants to produce a new "definable cohomology theory" which, unlike its classical counterpart, provides a complete classification to homotopy classes of mapping telescopes of d-tori, and for homotopy classes of maps from mapping telescopes of d-tori to spheres. In the process, we will prove Ulam stability for quotients of Polish abelian non-archimedean groups G by Polishable subgroups H. A special case of our Ulam stability theorem answers a question of Kanovei and Reeken regarding quotients of the p-adic groups.
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