discipline 
Mathematics

subject 
Differential
topology 3

lecturers 
András Szűcs 
credits 
2 
period 
third semester 
curriculum 
The quadratic form of a 4kdimensional manifold, The story of the 4manifolds (without proofs, results of Donaldson and Freedman.) The signature is cobordism invariant, Lefschetz theorem, Euler class, Characteristic classes, Splitting theorem, Leray – Hirsch theorem, Existence of the classes wi and ci These casses as obstructions, The geometric meaning of w1, The top dimensional wi class and the Thom class, Applications: If there is an embedding of an nmanifold into Rn+k, then The normal wkclass vanishes. What is the minimal dimension q for which there is an embedding int Rq of a product of surfaces. The Thom isomorphism, Pontrjagin theorem (For a null cobordant manfold all the characteristic numbers vanish.) Gysin sequence, The cohomology ring of RPn, The Stiefel Whitney classes of projectiv spaces, If n is a power of 2, then RP n can not be immersed into R(2n2) and cannot be embedded into R2n1. The rang of 8 dimensional cobordism group, 
literature 

form of tuition 
Lectures 
mode of assessment 
oral exam 