Nonorientable Lagrangian surfaces in rational 4-manifolds

Bo Dai, Chung I. Ho, Tian Jun Li

Research output: Contribution to journalArticlepeer-review

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We show that for any nonzero class A in H2(X;ℤ2) in a rational 4-manifold X, A is represented by a nonorientable embedded Lagrangian surface L (for some symplectic structure) if and only if P(A) ≡ ξ(L)(mod 4), where P(A) denotes the mod 4 valued Pontryagin square of A.

Original languageEnglish (US)
Pages (from-to)2837-2854
Number of pages18
JournalAlgebraic and Geometric Topology
Issue number6
StatePublished - 2019

Bibliographical note

Funding Information:
Acknowledgements Li would like to thank Banghe Li for useful discussions on Proposition 1.1. The research of Dai is partially supported by NSFC 11771232 and 11431001. The research of Ho is partially supported by MOST 105-2115-M-017-005-MY2. The research of Li is partially supported by the NSF.

Publisher Copyright:
© 2019, Mathematical Sciences Publishers. All rights reserved.


  • Lagrangian blowup
  • Nonorientable Lagrangian surface


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