TY  - JOUR
A1  - Seyedhosseini, Mehran
T1  - A variant of Roe algebras for spaces with cylindrical ends with applications in relative higher index theory
T2  - Journal of noncommutative geometry
N2  - In this paper, we define a variant of Roe algebras for spaces with cylindrical ends and use this to study questions regarding existence and classification of metrics of positive scalar curvature on such manifolds which are collared on the cylindrical end. 
We discuss how our constructions are related to relative higher index theory as developed by Chang, Weinberger, and Yu and use this relationship to define higher rho-invariants for positive scalar curvature metrics on manifolds with boundary. 
This paves the way for the classification of these metrics. 
Finally, we use the machinery developed here to give a concise proof of a result of Schick and the author, which relates the relative higher index with indices defined in the presence of positive scalar curvature on the boundary.
KW  - positive scalar curvature
KW  - higher index theory
KW  - rho-invariants
KW  - Roe algebras
KW  - manifolds with cylindrical ends
KW  - manifolds with boundary
Y1  - 2022
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/65183
SN  - 1661-6952
SN  - 1661-6960
VL  - 16
IS  - 2
SP  - 595
EP  - 624
PB  - European Mathematical Society
CY  - Zurich
ER  -