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Community Bot
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The Riemann-Roch theorem (and HRR, GRR, GRR for stacks, etc), over $\mathbb{C}$, associates topological information on one side $\chi(X,F)$, the Euler characteristic, to analytic information on the other side. If you want to relate analysis to topology, the biggest, baddest tool in your arsenal is The Atiyah-Singer Index TheoremThe Atiyah-Singer Index Theorem. Then it's just a matter of finding an operator that shows up naturally that should apply. In my answer on that one, I linked to the original paper, where Atiyah and Singer explicitly do HRR as Theorem 3.

The Riemann-Roch theorem (and HRR, GRR, GRR for stacks, etc), over $\mathbb{C}$, associates topological information on one side $\chi(X,F)$, the Euler characteristic, to analytic information on the other side. If you want to relate analysis to topology, the biggest, baddest tool in your arsenal is The Atiyah-Singer Index Theorem. Then it's just a matter of finding an operator that shows up naturally that should apply. In my answer on that one, I linked to the original paper, where Atiyah and Singer explicitly do HRR as Theorem 3.

The Riemann-Roch theorem (and HRR, GRR, GRR for stacks, etc), over $\mathbb{C}$, associates topological information on one side $\chi(X,F)$, the Euler characteristic, to analytic information on the other side. If you want to relate analysis to topology, the biggest, baddest tool in your arsenal is The Atiyah-Singer Index Theorem. Then it's just a matter of finding an operator that shows up naturally that should apply. In my answer on that one, I linked to the original paper, where Atiyah and Singer explicitly do HRR as Theorem 3.

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Charles Siegel
Charles Siegel
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The Riemann-Roch theorem (and HRR, GRR, GRR for stacks, etc), over $\mathbb{C}$, associates topological information on one side $\chi(X,F)$, the Euler characteristic, to analytic information on the other side. If you want to relate analysis to topology, the biggest, baddest tool in your arsenal is The Atiyah-Singer Index Theorem. Then it's just a matter of finding an operator that shows up naturally that should apply. In my answer on that one, I linked to the original paper, where Atiyah and Singer explicitly do HRR as Theorem 3.