Memoirs of the American Mathematical Society
2003;
58 pp;
Softcover
MSC: Primary 53;
Secondary 57
Print ISBN: 978-0-8218-3315-5
Product Code: MEMO/164/779
List Price: $52.00
AMS Member Price: $31.20
MAA Member Price: $46.80
Electronic ISBN: 978-1-4704-0377-5
Product Code: MEMO/164/779.E
List Price: $52.00
AMS Member Price: $31.20
MAA Member Price: $46.80
\(h\)-Principles and Flexibility in Geometry
Share this pageHansjörg Geiges
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 that allow one to prove \(h\)-principles. These notes, based on lectures given in the Graduiertenkolleg of Leipzig University, present two such methods which are strong enough to deal with applications (i) and (iii).
Readership
Graduate students and research mathematicians interested in geometry and topology.