Homological Algebra of Novikov-shubin Invariants and Morse Inequalities

  title={Homological Algebra of Novikov-shubin Invariants and Morse Inequalities},
  author={M. Farber},
It is shown in this paper that the topological phenomenon ”zero in the continuous spectrum”, discovered by S.P.Novikov and M.A.Shubin, can be explained in terms of a homology theory on the category of finite polyhedra with values in certain abelian category. This approach implies homotopy invariance of the Novikov-Shubin invariants. Its main advantage is that it allows to use the standard homological techniques, such as spectral sequences, derived functors, universal coefficients etc., while… CONTINUE READING
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