Codimension 2 transfer of signatures in L theory
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866918187882250240 |
|---|---|
| author | Luo, Yuetong |
| author_facet | Luo, Yuetong |
| contents | 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 $4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_22624 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Codimension 2 transfer of signatures in L theory Luo, Yuetong Geometric Topology Algebraic Topology 57R20 (primary), 57R67 (secondary) 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 $4$. |
| title | Codimension 2 transfer of signatures in L theory |
| topic | Geometric Topology Algebraic Topology 57R20 (primary), 57R67 (secondary) |
| url | https://arxiv.org/abs/2510.22624 |