# The Gromoll filtration, KO–characteristic classes and metrics of positive scalar curvature

@inproceedings{Crowley2013TheGF,
title={The Gromoll filtration, KO–characteristic classes and metrics of positive scalar curvature},
author={Diarmuid J. Crowley and Thomas Schick},
year={2013}
}
• Published 2013
• Mathematics
• Let X be a closed m-dimensional spin manifold which admits a metric of positive scalar curvature and let Pos(X) be the space of all such metrics. For any g in Pos(X), Hitchin used the KO-valued alpha-invariant to define a homomorphism A_{n-1} from \pi_{n-1}(Pos(X) to KO_{m+n}. He then showed that A_0 is not 0 if m = 8k or 8k+1 and that A_1 is not 0 if m = 8k-1 or 8\$. In this paper we use Hitchin's methods and extend these results by proving that A_{8j+1-m} is not 0 whenever m>6 and 8j - m… CONTINUE READING

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#### References

##### Publications referenced by this paper.
SHOWING 1-10 OF 28 REFERENCES

## Groups with torsion, bordism and rho invariants

• Mathematics
• 2007
VIEW 1 EXCERPT

## The Eta Invariant and Metrics of Positive Scalar Curvature

• BOTVINNIKPETER B. GILKEYyAbstract
• 1995
VIEW 1 EXCERPT

## DIFFERENTIABLE SPHERE BUNDLES

VIEW 2 EXCERPTS

## A counterexample to the (unstable) Gromov–Lawson–Rosenberg conjecture

VIEW 1 EXCERPT

## Smoothings of piecewise linear manifolds

• Mathematics
• 1974
VIEW 1 EXCERPT

## Generalized Poincare's Conjecture in Dimensions Greater Than Four

VIEW 6 EXCERPTS
HIGHLY INFLUENTIAL

## The homotopy type of the space of diffeomorphisms. II

• Mathematics
• 1974

## The classifying spaces for surgery and cobordism of manifolds

• Mathematics
• 1979