Taiwanese Journal of Mathematics

Sums of Recursion Operators

Hai-Long Her

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Let $(M,\omega,\tau)_A$ be a $2n$-dimensional smooth manifold with a pair of symplectic forms $\omega$ and $\tau$ intertwined by a recursion operator $A \in \operatorname{End}(TM)$. We consider a codimension two submanifolds $Q \subset M$ with those restricted symplectic forms $(\omega|_Q,\tau|_Q)$. Assume that $TQ$ is $A$-invariant. We call the tuple $(M,\omega,\tau,Q)_A$ symplectic-recursion data. In this paper, we consider the problem of fibre connected sum of such two symplectic-recursion data $(M_0,\omega_0,\tau_0,Q_0)_{A_0}$ and $(M_1,\omega_1,\tau_1,Q_1)_{A_1}$. It is interesting to consider potential applications of this result to integrable systems and mathematical string theory.

Article information

Taiwanese J. Math. Volume 21, Number 4 (2017), 753-766.

Received: 31 May 2016
Revised: 15 October 2016
Accepted: 23 October 2016
First available in Project Euclid: 27 July 2017

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Digital Object Identifier

Primary: 37J05: General theory, relations with symplectic geometry and topology 53D05: Symplectic manifolds, general

fibre connected sum recursion operator


Her, Hai-Long. Sums of Recursion Operators. Taiwanese J. Math. 21 (2017), no. 4, 753--766. doi:10.11650/tjm/7827. https://projecteuclid.org/euclid.twjm/1501120833

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