discipline 
MSC in Mathematics, Pure Mathematics,
Elective Course

subject 
Differential Forms

lecturers 
Dr. Balázs Csikós (associate professor) Dr. Gyula Lakos (assistant) Dr. Gábor Moussong (assistant professor) Dr. László Verhóczki (associate professor) 
credits 
2 
period 
3rd semester 
curriculum 
The notion of ordinary de Rham cohomology and de
Rham cohomology with compact supports. Poincarélemma. Algebraic homotopies
of complexes. MayerVietoris sequence. Poncaré pairing. Poincaré duality. Künneth
theorem. LerayHirsch theorem. Fiber bundles, cohomology with vertically
compact supports. Thom isomorphism theorem. Thom forms. Poincaré dual of
submanifolds. Multiplicative structure of cohomology. Intersections. Pfaff
forms, MathaiQuillen form. Euler form, PoincaréHopf theorem. Hodge operator. Hodge Laplacian. Harmonic forms.
The Hodge decomposition theorem on compact manifolds. Čech cohomology. The Čechde
Rham complex. Isomorphism of de Rham cohomology and Čech cohomology with real
coefficients. 
literature 
R. Bott – L. W. Tu: Differential forms in algebraic
geometry. Springer Verlag, F. W. Warner: Foundations of differentiable
manifolds and Lie groups. Springer Verlag, 
form of tuition 
Two hours
of lecture per week. 
mode of assessment 
oral exam 