$Pin^c$ and Lipschitz structures on products of manifolds

Details $Pin^c$ and Lipschitz structures on products of manifolds $Pin^c$ and Lipschitz structures on products of manifolds

2005-07-16

arxiv.org/abs/math/0507340v1

Annals of Global Analysis and Geometry 22 (2002), 291-300

Mathematics

Differential Geometry

10 pages

Scientific paper

The topological condition for the existence of a $pin^c$ structure on the product of two Riemannian manifolds is derived and applied to construct examples of manifolds having the weaker Lipschitz structure, but no $pin^c$ structure. An example of a five-dimensional manifold with this property is given; it is pointed out that there are no manifolds of lower dimension with this property.

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