Work

Generalised Winding Numbers With Applications to the K -theory of Adelic and Rational Group C * -algebras

Year: 2026

Type: article

Abstract: We establish a two-part framework for analysing homotopy equivalence in periodic adelic functions. First, we introduce the concept of pre-periodic functions and define their homotopy invariant through the construction of a generalised winding number. Second, we establish a fundamental correspondence between periodic adelic functions and pre-periodic functions. By extending the generalised winding number to periodic adelic functions, we demonstrate that this invariant completely characterises homotopy equivalence classes within the space of periodic adelic functions. Building on this classification, we further obtain an explicit description of the $K_{1}$ -group of the rational group $C^\ast $ -algebra, $K_{1}(C^{*}(\mathbb {Q}))$ . Finally, we employ a similar strategy to derive the K -theory of $C^{\ast }(\mathbb {A})$ .

Source: Bulletin of the Australian Mathematical Society

DOI: 10.1017/s0004972726101178

Authors: HANG WANG, WENQING WU

Institution: East China Normal University

Language: English

Topic: Advanced Operator Algebra Research

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,550

Funders: National Natural Science Foundation of China, Science and Technology Commission of Shanghai Municipality