Geometry Seminar

Voorjaarssemester 2001

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

The notion of homotopy principle or h-principle is one of the key concepts in an elegant language developed by Gromov to deal with a host of questions in geometry and topology. Roughly speaking, for a certain differential geometric problem to satisfy the h-principle is equivalent to saying that a solution to the problem exists whenever certain obvious topological obstructions vanish.

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 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.