Editing Atiyah–Singer index theorem (section)

===Teleman index theorem===
Due to  {{harv|Teleman|1983}}, {{harv|Teleman|1984}}:

:'''For any abstract elliptic operator {{harv|Atiyah|1970}} on a closed, oriented, topological manifold, the analytical index equals the topological index.'''
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 differentiability statement, but rather a topological statement.