Editing Chern–Gauss–Bonnet theorem (section)

=== Odd dimensions ===
The Chern formula is only defined for even dimensions because the [[Euler characteristic]] vanishes for odd dimensions. There is some research being done on 'twisting' the index theorem in [[K-theory]] to give non-trivial results for odd dimensions.<ref>{{Cite web |url=https://math.stackexchange.com/q/163287 |title=Why does the Gauss-Bonnet theorem apply only to even number of dimensons? |website=Mathematics Stack Exchange |date=June 26, 2012 |access-date=2019-05-08 }}</ref><ref>{{Cite arXiv <!-- |url=https://www.maths.ed.ac.uk/~v1ranick/papers/li4.pdf --> |title=The Gauss–Bonnet–Chern Theorem on Riemannian Manifolds|last=Li|first=Yin|year=2011|class=math.DG|eprint=1111.4972}}</ref>

There is also a version of Chern's formula for [[orbifold]]s.<ref>{{Cite web |url=https://mathoverflow.net/q/53302 |title=Is there a Chern-Gauss-Bonnet theorem for orbifolds? |website=MathOverflow |date=June 26, 2011 |access-date=2019-05-08}}</ref>