Voorjaarssemester 2001

Mondays, 16.00-17.30, room WI 401, begin: 29 January

The notion of

The foundational examples for applications of Gromov's ideas include
(i) Hirsch-Smale immersion theory,
(ii) Nash-Kuiper C ^{1}-isometric immersion theory,
(iii) existence of symplectic and contact structures on open manifolds.

Gromov has developed several powerful methods to prove h-principles. In this seminar we want to discuss two of these: the covering homotopy method and convex integration theory.

Students receive credit (7 stp.) for giving one of the 90 min. presentations. The first four lectures (after the introductory survey) require as background knowledge only a first course in manifold theory. Please contact H.Geiges if you are interested in participating actively.

Main source for this seminar will be the book *Embeddings and
Immersions* by M.Adachi (on order).

**N.B.**The previously announced seminar on geometries of surfaces
and 3-manifolds will not take place.

29.01.01 | H. Geiges | Introduction to Gromov's language of partial differential relations and h-principles | |||||

05.02.01 | M. Sandon | Regular closed curves in the plane | |||||

12.02.01 | K. van Winden | Jet bundles | |||||

19.02.01 | F. Pasquotto | Morse functions and handlebody decompositions | |||||

26.02.01 | K. Niederkrüger | Spaces of maps and their topologies | |||||

05.03.01 | F. Pasquotto | The h-principle for open, invariant relations I | |||||

12.03.01 | K. Niederkrüger | The h-principle for open, invariant relations II | |||||

19.03.01 | H. Geiges | The h-principle for open, invariant relations III | |||||

26.03.01 | H. Geiges | Convex integration theory | |||||

02.04.01 | O. van Koert | Complex structures on open manifolds I | |||||

23.04.01 | O. van Koert / M. Lübke | Complex structures on open manifolds II |

*
F. Pasquotto, January 8, 2001.
*