The Riemann–Roch theorem is an important theorem in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension...

a Riemann–Roch theorem for smooth manifolds is a version of results such as the Hirzebruch–Riemann–Roch theorem or Grothendieck–Riemann–Roch theorem (GRR)...

complex manifolds, which is itself a generalisation of the classical Riemann–Roch theorem for line bundles on compact Riemann surfaces. Riemann–Roch type...

examples included the Riemann–Roch theorem and its generalization the Hirzebruch–Riemann–Roch theorem, and the Hirzebruch signature theorem. Friedrich Hirzebruch...

theorem Riemann–Roch theorem for smooth manifolds Riemann–Roch theorem for surfaces Grothendieck–Hirzebruch–Riemann–Roch theorem Hirzebruch–Riemann–Roch...

Riemann–Roch theorem for smooth manifolds (differential topology) Riemann–Roch theorem for surfaces (algebraic surfaces) Riemann singularity theorem (algebraic...

see Chern–Weil homomorphism). The Riemann–Roch theorem can also be seen as a generalization of GB to complex manifolds. A far-reaching generalization that...

Riemann–Roch theorem and the Atiyah–Singer index theorem are other generalizations of the Gauss–Bonnet theorem. One useful form of the Chern theorem is...

earliest of a whole series of theorems (e.g. Atiyah–Singer index theorem, De Rham's theorem, Grothendieck–Riemann–Roch theorem) establishing deep relationships...

cohomology. For smooth projective varieties, Serre duality can be viewed as an analog of Poincaré duality. It also leads to the Riemann–Roch theorem for projective...