Stephan Stolz

A diffeomorphism classification of 7-dimensional homogeneous Einstein manifolds with SU(3) X SU(2) X U(1)-symmetry

On donne des exemples qui montrent que des espaces homogenes homeomorphes ne sont pas necessairement diffeomorphes

NONCONNECTED MODULI SPACES OF POSITIVE SECTIONAL CURVATURE METRICS

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 acts on these spaces. We construct examples of 7-dimensional manifolds for which the moduli space 9\~(M)/ Diff(M) is not connected and others for which 9\~c(M)/ Diff(M) has infinitely many connected components. The examples are obtained by analyzing a family of positive sectional curvature metrics on homogeneous spaces constructed by Aloff and Wallach, on which SU(3) acts transitively, respectively a family of positive Einstein metrics constructed by Wang and Ziller on homogeneous spaces, on which SU(3) x SU(2) x U(I) acts transitively. MAX-PLANCK-INSTITUT FUR MATHEMATIK, GOTTFRIED-CLAREN-STRASSE 26, 5300 BONN 3, GERMANY AND FACHBEREICH MATHEMATIK, UNIVERSITAT MAINZ, 6500 MAINZ, GERMANY Current address: Johannes Gutenberg Universitat Mainz, Fachbereich Mathematik, Staudinger- weg 9, 6500 Mainz, Germany E-mail address:kreck@topologie.mathematik.uni-mainz.de DEPARTMENT OF MATHEMATICS, UNIVERSITY OF NOTRE DAME, NOTRE DAME, INDIANA 46556 E-mail address: stolz.l@nd.edu License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use

Manifolds of Positive Scalar Curvature

We survey the status of the problem of determining which differentiable manifolds (without boundary) have Riemannian metrics of positive scalar curvature. Of course, if the manifold is non-compact, one requires the metric to be complete.

Positive Scalar Curvature Metrics — Existence and Classification Questions

Let M be an n-dimensional manifold (all manifolds considered in this paper are smooth, compact, and, unless otherwise specified, their boundary is empty).

Differential forms and 0-dimensional super symmetric field theories

We show that closed differential forms on a smooth manifold X can be interpreted astopological(respectivelyEudlidean)supersymmetricfieldtheoriesofdimension0j1overX. As a consequence, concordance classes of such field theories are shown to represent de Rham cohomology. The main contribution of this paper is to make all new mathematical notions regarding supersymmetric field theories precise.