THE GROMOV-LAWSON-ROSENBERG CONJECTURE FOR THE SEMI-DIHEDRAL GROUP OF ORDER 16
نویسندگان
چکیده
منابع مشابه
Gromov-Lawson-Rosenberg conjecture
Doing surgery on the 5-torus, we construct a 5-dimensional closed spin-manifold M with π1(M) ∼= Z ×Z/3, so that the index invariant in the KO-theory of the reduced C-algebra of π1(M) is zero. Then we use the theory of minimal surfaces of Schoen/Yau to show that this manifolds cannot carry a metric of positive scalar curvature. The existence of such a metric is predicted by the (unstable) Gromov...
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vanishes Note that index D M unlike the dimension of the ker nel and the dimension of the cokernel of D M is independent of the metric used in the construction of D M In fact according to the Atiyah Singer Index Theorem it is equal to a topological invariant A M the A genus ofM cf Ch III Thm We recall that A M is a characteristic number de ned by evaluating a certain polyno mial in the Pontrjag...
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The Gromov-Lawson-Rosenberg (GLR)-conjecture for a group Γ states that a closed spin manifold M (n ≥ 5) with fundamental group Γ admits a metric with scal > 0 if and only if its C-index α(M) ∈ KOn(C ∗ red (Γ)) vanishes. We prove this for groups Γ with lowdimensional classifying space and products of such groups with free abelian groups, provided the assembly map for the group Γ is (split) injec...
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Gromov and Lawson conjectured in [GL2] that a closed spin manifold M of dimension n with fundamental group π admits a positive scalar curvature metric if and only if an associated element in KOn(Bπ) vanishes. In this note we present counter examples to the ‘if’ part of this conjecture for groups π which are torsion free and whose classifying space is a manifold with negative curvature (in the A...
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 2014
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089514000342