Usuária:Francieli Triches/Testes: diferenças entre revisões

In 1948 [[Edwin Spanier]], building on work of Alexander and Kolmogorov, developed [[Alexander–Spanier cohomology]].

 

'''[[Sheaf cohomology]]''' is a rich generalization of singular cohomology, allowing more general "coefficients" than simply an abelian group. For every [[sheaf (mathematics)|sheaf]] of abelian groups ''E'' on a topological space ''X'', one has cohomology groups ''H''^''i''(''X'',''E'') for integers ''i''. In particular, in the case of the [[constant sheaf]] on ''X'' associated to an abelian group ''A'', the resulting groups ''H''^''i''(''X'',''A'') coincide with singular cohomology for ''X'' a manifold or CW complex (though not for arbitrary spaces ''X''). Starting in the 1950s, sheaf cohomology has become a central part of [[algebraic geometry]] and [[complex analysis]], partly because of the importance of the sheaf of [[regular function]]s or the sheaf of [[holomorphic function]]s.