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These lecture notes contain a guided tour to the Novikov Conjecture and related conjectures due to Baum-Connes, Borel and Farrell-Jones. They begin with basics about higher signatures, Whitehead torsion and the s-Cobordism Theorem. Then an introduction to surgery theory and a version of the assembly map is presented. Using the solution of the Novikov conjecture for special groups some applications to the classification of low dimensional manifolds are given.

K-theory --- Noncommutative differential geometry --- Differential topology --- K-théorie --- Géométrie différentielle non commutative --- Topologie différentielle --- Congresses. --- Congrès --- Novikov conjecture --- Differential topology -- Congresses. --- K-theory -- Congresses. --- Noncommutative differential geometry -- Congresses. --- Novikov conjecture -- Congresses. --- Geometry --- Mathematics --- Physical Sciences & Mathematics --- K-théorie --- Géométrie différentielle non commutative --- Topologie différentielle --- Congrès --- EPUB-LIV-FT LIVMATHE SPRINGER-B --- Differential geometry, Noncommutative --- Geometry, Noncommutative differential --- Non-commutative differential geometry --- Conjecture, Novikov --- Novikov's conjecture --- Mathematics. --- Algebraic topology. --- Manifolds (Mathematics). --- Complex manifolds. --- Algebraic Topology. --- Manifolds and Cell Complexes (incl. Diff.Topology). --- Geometry, Differential --- Topology --- Infinite-dimensional manifolds --- Operator algebras --- Manifolds (Mathematics) --- Cell aggregation --- Aggregation, Cell --- Cell patterning --- Cell interaction --- Microbial aggregation --- Analytic spaces --- Novikov conjecture - Congresses --- K-theory - Congresses --- Noncommutative differential geometry - Congresses --- Differential topology - Congresses