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Gromov $K\mkern-4mu$–area and jumping curves in $\mathbb{CP}^n$

Yasha Savelyev

Algebraic & Geometric Topology 12 (2012) 2317–2327
Abstract

We give here some extensions of Gromov’s and Polterovich’s theorems on k–area of n, particularly in the symplectic and Hamiltonian context. Our main methods involve Gromov–Witten theory, and some connections with Bott periodicity and the theory of loop groups. The argument is closely connected with the study of jumping curves in n, and as an upshot we prove a new symplectic-geometric theorem on these jumping curves.

Keywords
Gromov $K$–area, Gromov–Witten theory, jumping curves
Mathematical Subject Classification 2010
Primary: 53D45
References
Publication
Received: 11 June 2012
Revised: 6 September 2012
Accepted: 23 September 2012
Published: 8 January 2013
Authors
Yasha Savelyev
Centre de Recherches Mathématiques
Université de Montréal
P.O. Box 6128
Centre-ville Station
Montréal H3C 3J7
Canada
https://sites.google.com/site/yashasavelyev/