The Chern conjecture for affinely flat manifolds using combinatorial methods

Cited 0 time in webofscience Cited 0 time in scopus
  • Hit : 469
  • Download : 1
An affine manifold is a manifold with a flat affine structure, i.e. a torsion-free. at affine connection. We slightly generalize the result of Hirsch and Thurston that if the holonomy of a closed affine manifold is isomorphic to amenable groups amalgamated or HNN-extended along finite groups, then the Euler characteristic of the manifold is zero confirming an old conjecture of Chern. The technique is from Kim and Lee's work using the combinatorial Gauss-Bonnet theorem and taking the means of the angles by amenability. We show that if an even-dimensional manifold is obtained from a connected sum operation from K(pi,1)s with amenable fundamental groups, then the manifold does not admit an affine structure generalizing a result of Smillie.
Publisher
SPRINGER
Issue Date
2003-03
Language
English
Article Type
Article
Citation

GEOMETRIAE DEDICATA, v.97, no.1, pp.81 - 92

ISSN
0046-5755
DOI
10.1023/A:1023664521970
URI
http://hdl.handle.net/10203/7626
Appears in Collection
MA-Journal Papers(저널논문)
Files in This Item

qr_code

  • mendeley

    citeulike


rss_1.0 rss_2.0 atom_1.0