Annals of K-Theory

Positive scalar curvature and low-degree group homology

Noé Bárcenas and Rudolf Zeidler

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Let Γ be a discrete group. Assuming rational injectivity of the Baum–Connes assembly map, we provide new lower bounds on the rank of the positive scalar curvature bordism group and the relative group in Stolz’ positive scalar curvature sequence for B Γ . The lower bounds are formulated in terms of the part of degree up to 2 in the group homology of Γ with coefficients in the Γ -module generated by finite order elements. Our results use and extend work of Botvinnik and Gilkey which treated the case of finite groups. Further crucial ingredients are a real counterpart to the delocalized equivariant Chern character and Matthey’s work on explicitly inverting this Chern character in low homological degrees.

Article information

Ann. K-Theory, Volume 3, Number 3 (2018), 565-579.

Received: 3 October 2017
Revised: 21 December 2017
Accepted: 6 January 2018
First available in Project Euclid: 24 July 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 58D27: Moduli problems for differential geometric structures 58J22: Exotic index theories [See also 19K56, 46L05, 46L10, 46L80, 46M20]
Secondary: 19K33: EXT and $K$-homology [See also 55N22] 19L10: Riemann-Roch theorems, Chern characters 19L47: Equivariant $K$-theory [See also 55N91, 55P91, 55Q91, 55R91, 55S91] 55N91: Equivariant homology and cohomology [See also 19L47]

positive scalar curvature secondary index theory $\rho$-invariant equivariant Chern character group homology


Bárcenas, Noé; Zeidler, Rudolf. Positive scalar curvature and low-degree group homology. Ann. K-Theory 3 (2018), no. 3, 565--579. doi:10.2140/akt.2018.3.565.

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