Nonpositive curvature exercise

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1 total messages Started by Mark Cassorla Wed, 30 Dec 1992 23:29

#939

Author: Mark Cassorla
Date: Wed, 30 Dec 1992 23:29

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The following exercise appears in "Manifolds of Nonpositive Curvature".
Any hints or solutions would be appreciated.  (Note: This is the
first exercise in the book so I think it is easily solved, but my 
head must be screwed in incorrectly.)

Let S be a surface of genus>=2 and let V=SxS.  If D is the diagonal
in V and W is a 4-manifold that admits a local diffeo over V-D that
is ramified at D, show that W admits no smooth metric of nonpositive
curvature.

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