Homotopy colimits and cohomology with local coefficients
Hyperhopfian groups and approximate fibrations
Lefschetz-Riemann-Roch theorem and coherent trace formula.
Lokalisierung äquivarianter Kohomologie-Theorien.
Mayer-Vietoriss Sequences for HNN-Groups and Homological Duality.
Nilpotency of self homotopy equivalences with coefficients
In this paper we study the nilpotency of certain groups of self homotopy equivalences. Our main goal is to extend, to localized homotopy groups and/or homotopy groups with coefficients, the general principle of Dror and Zabrodsky by which a group of self homotopy equivalences of a finite complex which acts nilpotently on the homotopy groups is itself nilpotent.
Nonresonance conditions for arrangements
We prove a vanishing theorem for the cohomology of the complement of a complex hyperplane arrangement with coefficients in a complex local system. This result is compared with other vanishing theorems, and used to study Milnor fibers of line arrangements, and hypersurface arrangements.
Normalisation for the fundamental crossed complex of a simplicial set.
Novikov homology, jump loci and Massey products
Let X be a finite CW complex, and ρ: π 1(X) → GL(l, ℂ) a representation. Any cohomology class α ∈ H 1(X, ℂ) gives rise to a deformation γ t of ρ defined by γ t (g) = ρ(g) exp(t〈α, g〉). We show that the cohomology of X with local coefficients γ gen corresponding to the generic point of the curve γ is computable from a spectral sequence starting from H*(X, ρ). We compute the differentials of the spectral sequence in terms of the Massey products and show that the spectral sequence degenerates in case...
On a Conjecture of Bredon.
On dimensions in Bredon homology.
On Injective Rational Coefficient Systems.
On localization in holomorphic equivariant cohomology
We study a holomorphic equivariant cohomology built out of the Atiyah algebroid of an equivariant holomorphic vector bundle and prove a related localization formula. This encompasses various residue formulas in complex geometry, in particular we shall show that it contains as special cases Carrell-Liebermann’s and Feng-Ma’s residue formulas, and Baum-Bott’s formula for the zeroes of a meromorphic vector field.
Some analogs of Zariski's Theorem on nodal line arrangements.
Strong surjectivity of mappings of some 3-complexes into 3-manifolds
Let K be a CW-complex of dimension 3 such that H³(K;ℤ) = 0, and M a closed manifold of dimension 3 with a base point a ∈ M. We study the problem of existence of a map f: K → M which is strongly surjective, i.e. such that MR[f,a] ≠ 0. In particular if M = S¹ × S² we show that there is no f: K → S¹ × S² which is strongly surjective. On the other hand, for M the non-orientable S¹-bundle over S² there exists a complex K and f: K → M such that MR[f,a] ≠ 0.
Strong surjectivity of mappings of some 3-complexes into
Let K be a CW-complex of dimension 3 such that H 3(K;ℤ) = 0 and the orbit space of the 3-sphere with respect to the action of the quaternion group Q 8 determined by the inclusion Q 8 ⊆ . Given a point a ∈ , we show that there is no map f:K → which is strongly surjective, i.e., such that MR[f,a]=min(g −1(a))|g ∈ [f] ≠ 0.
Structural Theorems for Topological Actions of Z...-Tori on Real, Complex and Quarternionic Projective Spaces
Tetrahedra on deformed spheres and integral group cohomology.
The abelianization of the Johnson kernel
We prove that the first complex homology of the Johnson subgroup of the Torelli group is a non-trivial, unipotent -module for all and give an explicit presentation of it as a -module when . We do this by proving that, for a finitely generated group satisfying an assumption close to formality, the triviality of the restricted characteristic variety implies that the first homology of its Johnson kernel is a nilpotent module over the corresponding Laurent polynomial ring, isomorphic to the...
The cyclic groups and the free loop space.