Mathematics – Differential Geometry
Scientific paper
1995-03-16
Mathematics
Differential Geometry
45 pages, plain TEX(LATEX for the Katzarkov's appendix)
Scientific paper
From the cohomological point of view the symplectomorphism group $Sympl (M)$ of a symplectic manifold is `` tamer'' than the diffeomorphism group. The existence of invariant polynomials in the Lie algebra $\frak {sympl }(M)$, the symplectic Chern-Weil theory, and the existence of Chern-Simons-type secondary classes are first manifestations of this principles. On a deeper level live characteristic classes of symplectic actions in periodic cohomology and symplectic Hodge decompositions. The present paper is called to introduce theories and constructions listed above and to suggest numerous concrete applications. These includes: nonvanishing results for cohomology of symplectomorphism groups (as a topological space, as a topological group and as a discrete group), symplectic rigidity of Chern classes, lower bounds for volumes of Lagrangian isotopies, the subject started by Givental, Kleiner and Oh, new characters for Torelli group and generalizations for automorphism groups of one-relator groups, arithmetic properties of special values of Witten zeta-function and solution of a conjecture of Brylinski. The Appendix, written by L. Katzarkov, deals with fixed point sets of finite group actions in moduli spaces.
No associations
LandOfFree
Characteristic Classes in Symplectic Topology does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Characteristic Classes in Symplectic Topology, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Characteristic Classes in Symplectic Topology will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-688531