The chern-classes tag has no wiki summary.

**12**

votes

**0**answers

585 views

### Poincare-Hopf and Matthai-Quillen for Chern classes?

One. The Poincare-Hopf theorem is usually stated as a formula for the Euler characteristic of the tangent bundle TM. Is there a version for Euler classes, of oriented real vector bundles?
It seems ...

**7**

votes

**3**answers

1k views

### on chern classes and Riemann Roch theorem for torsion-free sheaves on singular (possibly multiple) curve

I'm looking for a definition of Chern class (at least the first one) for a torsion-free sheaf $F$ (not necessarily locally free) on a singular curve (for simplicity can assume all the singularities ...

**4**

votes

**1**answer

248 views

### Does the non-commutative Chern class depend on the choice of connection?

In classical geometry the calculation of the Chern classes of a vector bundle using a connection is independent of the choice of connection. Does any such result hold for projective modules in ...