Volume 13, issue 2 (2009)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 25, 1 issue

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
Other MSP Journals
Novikov-symplectic cohomology and exact Lagrangian embeddings

Alexander F Ritter

Geometry & Topology 13 (2009) 943–978

Let N be a closed manifold satisfying a mild homotopy assumption. Then for any exact Lagrangian L TN the map π2(L) π2(N) has finite index. The homotopy assumption is either that N is simply connected, or more generally that πm(N) is finitely generated for each m 2. The manifolds need not be orientable, and we make no assumption on the Maslov class of L.

We construct the Novikov homology theory for symplectic cohomology, denoted SH(M;L¯α), and we show that Viterbo functoriality holds. We prove that the symplectic cohomology SH(TN;L¯α) is isomorphic to the Novikov homology of the free loopspace. Given the homotopy assumption on N, we show that this Novikov homology vanishes when α H1(0N) is the transgression of a nonzero class in H2(Ñ). Combining these results yields the above obstructions to the existence of L.

symplectic homology, Novikov homology, exact Lagrangian
Mathematical Subject Classification 2000
Primary: 57R17
Secondary: 57R58
Received: 13 November 2007
Revised: 24 December 2008
Accepted: 21 December 2008
Published: 8 January 2009
Proposed: Simon Donaldson
Seconded: Jim Bryan, Ron Stern
Alexander F Ritter
Department of Mathematics
Cambridge, MA 02139