Adiabatic groupoid and secondary invariants in K-theory

Zenobi, Vito Felice

doi:10.1016/j.aim.2019.03.003

Cited by 8 publications

(3 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [11, Section 5] Piazza and Schick construct a map from the Stolz exact sequence to the Higson-Roe exact sequence (see also [20,23] for different approaches). Instead of working with complex C * -algebras as in [11], one can without extra effort adapt this construction to the setting of real C * -algebras (compare [22]).…”

Section: Mapping Psc To Analysis To Detect Bordism Classesmentioning

confidence: 99%

Positive Scalar Curvature due to the Cokernel of the Classifying Map

Schick,

Zenobi

2020

Preprint

Self Cite

View full text Add to dashboard Cite

This paper contributes to the classification of positive scalar curvature metrics up to bordism and up to concordance.Let M be a closed spin manifold of dimension ≥ 5 which admits a metric with positive scalar curvature. We give lower bounds on the rank of the group of psc metrics on M up to bordism in terms of the corank of the canonical map KO * (M) → KO * (Bπ 1 (M)), provided the rational analytic Novikov conjecture is true for π 1 (M).

show abstract

Section: Mapping Psc To Analysis To Detect Bordism Classesmentioning

confidence: 99%

Positive Scalar Curvature due to the Cokernel of the Classifying Map

Schick,

Zenobi

2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…In [15, Section 5] Piazza and Schick construct a map from the Stolz exact sequence to the Higson-Roe exact sequence (see also [24,27] for different approaches). Instead of working with complex C * -algebras as in [15], one can without extra effort adapt this construction to the setting of real C * -algebras (compare [26]).…”

Section: Mapping Psc To Analysis To Detect Bordism Classesmentioning

confidence: 99%

Positive Scalar Curvature due to the Cokernel of the Classifying Map

Schick

Zenobi

2020

SIGMA

Self Cite

View full text Add to dashboard Cite

“…We introduce next a secondary invariant which encodes information in K-theory about the structure of a given compatible metric of positive scalar curvature. See also [52] where secondary invariants are introduced that control the vanishing of the generalized index defined via the adiabatic groupoid, instead of the Fredholm index defined via the Fredholm groupoid. Consider first the following general setup: Let A, B be separable C * -algebras.…”

Section: Rescalingmentioning

confidence: 99%