Open AccessA C-symplectic free πΒΉ-manifold with contractible orbits and πππ=\frac12πππ
Author(s) -
Christopher Allday,
John Oprea
Publication year - 2005
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/s0002-9939-05-07945-1
Subject(s) - symplectic geometry , symplectic manifold , symplectomorphism , contractible space , mathematics , moment map , pure mathematics , action (physics) , symplectic representation , symplectic group , manifold (fluid mechanics) , symplectic vector space , topology (electrical circuits) , physics , combinatorics , quantum mechanics , mechanical engineering , engineering
An interesting question in symplectic geometry concerns whether or not a closed symplectic manifold can have a free symplectic circle action with orbits contractible in the manifold. Here we present a c-symplectic example, thus showing that the problem is truly geometric as opposed to topological. Furthermore, we see that our example is the only known example of a c-symplectic manifold having non-trivial fundamental group and Lusternik-Schnirelmann category precisely half its dimension.