11/21/08
http://arxiv.org/abs/math.AG/0512486
it write by Constantin Teleman and Christopher T. Woodward. submitted on 21 Dec 2005
this website is describe the chern classes and The Newstead-Ramanan conjecture for Chern classes.
The Chern classes of a complex manifold are the Chern classes of its tangent bundle. The 
th Chern class is anobstruction to the existence of 
everywhere complex linearly independent vector fields on that vector bundle. The 
th Chern class is in the 
th cohomology group of the base space.in topology, differential geometry, and algebraic geometry, it is often of vital importance to know how many linearly independent sections a vector bundle has. The Chern classes can be used to provide a great deal of information in answering this question.
th Chern class is anobstruction to the existence of everywhere complex linearly independent vector fields on that vector bundle. The th Chern class is in the th cohomology group of the base space.in topology, differential geometry, and algebraic geometry, it is often of vital importance to know how many linearly independent sections a vector bundle has. The Chern classes can be used to provide a great deal of information in answering this question. 
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