arXiv subjects

Yuetong Luo

Publications and source records attributed to Yuetong Luo.

2 recordsLinked to original sources

arXiv2025

Codimension 2 transfer of signatures in L theory

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 $4$.

math.GT↗

arXiv2025

Codimension 1 transfer maps of K theoretic indexes

Let $M$ be a closed spin manifold and $N$ be a codimension 1 submanifold of it. Given certain homotopy conditions, Zeidler shows that the Rosenberg index of $N$ is an obstruction to the existence of positive scalar curvature on $M$. He further gives a transfer map between the K groups of the group $C^*$ algebras of the foundemental group. The transfer map maps the Rosenberg index of $M$ to the one of $N$. In this note, we present an alternative formulation of the transfer map using maps between $C^*$ algebras, and give an analogus result for the codimension 1 transfer of higher K theoretic signatures.

math.KT↗