discipline

Mathematics

subject

Differential topology 3

lecturers

András Szűcs

credits

2

period

third semester

curriculum

The quadratic form of a 4k-dimensional manifold,

The story of the 4-manifolds (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 n-manifold into Rn+k, then

The normal wk-class 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(2n-2) and cannot be embedded into R2n-1.

The rang of 8 dimensional cobordism group,

literature

 

form of tuition

Lectures

mode of assessment

oral exam