2025/10/26 by Yuxia Luo, Luo, Yuetong
Mathematics · #57R20 (primary) #57R67 (secondary) #Advanced Operator Algebra Research #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2510.22624
openalex publication_date 2025/10/26 · openalex created_date 2025/10/29 · openalex updated_date 2026/07/28
The signature of a closed manifold is an important geometric topology. Let M be a closed manifold and N be a codimension 2 submanifold of it. Given certain homotopy conditions, Higson, Xie and Schick proved an invariance theorem in codimension 2 for the K-theoretic signature. They asked for the L-theoretic counterpart of their result. In this note, we will answer their question and moreover, construct a tranfer map between the symmetric L-groups of the fundamental groups of M and N, which carries the signature of M to that of N up to a torsion of order at most 4.