# Path-component invariants for spaces of positive scalar curvature metrics

@article{Wraith2016PathcomponentIF, title={Path-component invariants for spaces of positive scalar curvature metrics}, author={David J. Wraith}, journal={arXiv: Differential Geometry}, year={2016} }

The Kreck-Stolz s-invariant is a classic path-component invariant for the space and moduli space of positive scalar curvature metrics. It is an absolute (as opposed to relative) invariant, but this strength comes at the expense of being defined only under restrictive topological conditions. The aim of this paper is to construct an analogous invariant for certain product manifolds on which the s-invariant is not defined.

## One Citation

On the topology of moduli spaces of non-negatively curved Riemannian metrics

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- 2017

We study spaces and moduli spaces of Riemannian metrics with non-negative Ricci or non-negative sectional curvature on closed and open manifolds and construct, in particular, the first classes of…

## References

SHOWING 1-10 OF 30 REFERENCES

The space of metrics of positive scalar curvature

- Mathematics
- 2014

We study the topology of the space of positive scalar curvature metrics on high dimensional spheres and other spin manifolds. Our main result provides elements in higher homotopy and homology groups…

Deforming three-manifolds with positive scalar curvature

- Mathematics, Physics
- 2009

In this paper we prove that the moduli space of metrics with positive scalar curvature of an orientable compact 3-manifold is path-connected. The proof uses the Ricci flow with surgery, the conformal…

Homotopy groups of the moduli space of metrics of positive scalar curvature

- Mathematics
- 2010

We show by explicit examples that in many degrees in a stable range the homotopy groups of the moduli spaces of Riemannian metrics of positive scalar curvature on closed smooth manifolds can be…

Non-negative versus positive scalar curvature

- Mathematics
- 2016

We show that results about spaces or moduli spaces of positive scalar curvature metrics proved using index theory can typically be extended to non-negative scalar curvature metrics. We illustrate…

Moduli Spaces of Riemannian Metrics

- Mathematics
- 2015

Part I: Positive scalar curvature.- The (moduli) space of all Riemannian metrics.- Clifford algebras and spin.- Dirac operators and index theorems.- Early results on the space of positive scalar…

Nonconnected Moduli Spaces of Nonnegative Sectional Curvature Metrics on Simply Connected Manifolds

- Mathematics
- 2016

We show that in each dimension $4n+3$, $n\ge 1$, there exist infinite sequences of closed smooth simply connected manifolds $M$ of pairwise distinct homotopy type for which the moduli space of…

The moduli space of negatively curved metrics of a hyperbolic manifold

- Mathematics
- 2010

We prove that the moduli space of negatively curved metrics of a hyperbolic manifold M n has nontrivial homotopy and homology groups in certain dimensions (depending on n) provided M has a ‘good’…

Connectedness properties of the space of complete nonnegatively curved planes

- Mathematics
- 2013

We study the space of complete Riemannian metrics of nonnegative curvature on the plane equipped with the $$C^k$$Ck topology. If $$k$$k is infinite, we show that the space is homeomorphic to the…

Cobordism invariance of the homotopy type of the space of positive scalar curvature metrics

- Mathematics
- 2011

This is the publisher’s final pdf. The published article is copyrighted by the American Mathematical Society and can be found at: http://www.ams.org/publications/journals/journalsframework/proc.

NONCONNECTED MODULI SPACES OF POSITIVE SECTIONAL CURVATURE METRICS

- Mathematics
- 1993

For a closed manifold M let 9\~(M) (resp. 9\~ic(M)) be the space of Riemannian metrics on M with positive sectional (resp. Ricci) cur- vature and let Diff(M) be the diffeomorphism group of M, which…