Algebraic and differential topology

The scientific research principally regards problems related to topological and differentiable manifolds (and their generalizations) faced by techniques of Algebraic, Geometric and Differential Geometry, Combinatorial Theory of Groups,  Homological Algebra,  Knot Theory, and Graph Theory. The main goals of the research are to obtain the topological and homotopical classification of large classes of spaces (as manifolds, generalized manifolds, Poincare` complexes, structured polyhedra, etc.), to determine the cobordism class of them and to compute  their principal algebraic invariants. Using methods of Homological Algebra and L-Theory, we study several questions of Algebraic Surgery Theory on compact manifolds and of Dehn-Lickorish Surgery on knots and links. We also analyze the algebraic properties of the obstruction groups for Surgery and construct several spectral sequences which are very useful for the classification problems mentioned before. Finally, the representation of compact polyhedra by means of oriented and/or coloured graphs allows us to give combinatorial methods for the explicit computation of their algebraic and numerical invariants.

 

[Ultimo aggiornamento: 02/02/2021 09:24:17]