Atiyah–Singer index theorem: Difference between revisions

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The proof of this result goes through specific considerations, including the extension of Hodge theory on combinatorial and Lipschitz manifolds {{harv|Teleman|1980}}, {{harv|Teleman|1983}}, the extension of Atiyah–Singer's signature operator to Lipschitz manifolds {{harv|Teleman|1983}}, Kasparov's K-homology {{harv|Kasparov|1972}} and topological cobordism {{harv|Kirby|Siebenmann|1977}}.
 
This result shows that the index theorem is not merely a differentiabledifferentiability statement, but rather a topological statement.
 
===Connes–Donaldson–Sullivan–Teleman index theorem===