{"title":"(Semi)topological $K$-theory via solidification","authors":"Ko Aoki","doi":"arxiv-2409.01462","DOIUrl":null,"url":null,"abstract":"Clausen--Scholze introduced the notion of solid spectrum in their condensed\nmathematics program. We demonstrate that the solidification of algebraic\n$K$-theory recovers two known constructions: the semitopological $K$-theory of\na real (associative) algebra and the topological (aka operator) $K$-theory of a\nreal Banach algebra.","PeriodicalId":501136,"journal":{"name":"arXiv - MATH - Rings and Algebras","volume":"75 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Rings and Algebras","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.01462","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Clausen--Scholze introduced the notion of solid spectrum in their condensed
mathematics program. We demonstrate that the solidification of algebraic
$K$-theory recovers two known constructions: the semitopological $K$-theory of
a real (associative) algebra and the topological (aka operator) $K$-theory of a
real Banach algebra.
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