K-theory of relative group C^*-algebras and the relative Novikov conjecture

2021/10/21 by Jintao Deng, Deng, Jintao, Geng Tian +5
Mathematics · #19K33 #19K35 #19K56 #20F65 #20F67 #46L87 #47B02 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2110.10859

openalex publication_date 2021/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The relative Novikov conjecture states that the relative higher signatures of manifolds with boundary are invariant under orientation-preserving homotopy equivalences of pairs. In this paper, we study the relative Baum-Connes assembly map for any pair of groups and apply it to solve the relative Novikov conjecture when the groups satisfy certain geometric conditions.

Related

• Strong relative Novikov conjecture for coarsely embeddable groups
• The Baum--Connes conjecture localised at the unit element of a discrete\n group
• A description of the assembly map for the Baum-Connes conjecture with coefficients
• Exactness and the Novikov Conjecture
• Relative K-theory for C^*-algebras