Dan Burghelea
Published 2015-01-05Version 1
We propose a refinement of the Betti numbers of a compact ANR in the presence of a continuous function worked out in collaboration with Stefan Haller. The refinement consists of finite configurations of points with specified multiplicity located in the complex plane of cardinality (counted with multiplicity) the Betti numbers, equivalently of monic polynomials with complex coefficients of degree the Betti numbers of the space A number of properties are discussed (Theorems 4.1, 4.2 and 4.3) as well as the realization of each such configurations as dimensions of mutually orthogonal subspaces of the homology vector spaces, when equipped with a Hilbert space structure, indexed by the points of the configuration.
A refinement of Betti numbers and homology in the presence of a continuous function. II
On the minimal sum of Betti numbers of an almost complex manifold
Betti numbers of configuration spaces of surfaces
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