Rigidity Properties of Compact Lie Groups Modulo Maximal Tori.
The rational homotopy of Thom spaces and the smoothing of homology classes.
The rational homotopy of Thom spaces and the smoothing of isolated singularities
Rational homotopy methods are used for studying the problem of the topological smoothing of complex algebraic isolated singularities. It is shown that one may always find a suitable covering which is smoothable. The problem of the topological smoothing (including the complex normal structure) for conical singularities is considered in the sequel. A connection is established between the existence of certain relations between the normal Chern degrees of a smooth projective variety and the question...
Moduli spaces for fundamental groups and Link invariants derived from the lower central series.
Cohomologically generic 2-complexes and 3-dimensional Poincaré complexes.
Homotopy Lie algebras and fundamental groups via deformation theory
We formulate first results of our larger project based on first fixing some easily accessible invariants of topological spaces (typically the cup product structure in low dimensions) and then studying the variations of more complex invariants such as (the homotopy Lie algebra) or (the graded Lie algebra associated to the lower central series of the fundamental group). We prove basic rigidity results and give also an application in low-dimensional topology.
Equivariant chain complexes, twisted homology and relative minimality of arrangements
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...
Complex cohomology automorphisms of compact homogeneous spaces of positive Euler characteristic
Homotopy Lie algebras; lower central series and the Koszul property.
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