Nonorientable Lagrangian surfaces in rational 4–manifolds

Dai, Bo; Ho, Chung-I; Li, Tian-Jun

doi:10.2140/agt.2019.19.2837

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Nonorientable Lagrangian surfaces in rational $4$–manifolds

Bo Dai, Chung-I Ho and Tian-Jun Li

Algebraic & Geometric Topology 19 (2019) 2837–2854

DOI: 10.2140/agt.2019.19.2837

Abstract

We show that for any nonzero class $A$ in $H_{2} (X; ℤ_{2})$ in a rational $4 -$ manifold $X$ , $A$ is represented by a nonorientable embedded Lagrangian surface $L$ (for some symplectic structure) if and only if $P (A) \equiv χ (L) (mod 4)$ , where $P (A)$ denotes the mod $4$ valued Pontryagin square of $A$ .

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Keywords

nonorientable Lagrangian surface, Lagrangian blowup

Mathematical Subject Classification 2010

Primary: 53D12, 57Q35

References

Publication

Received: 25 August 2017

Revised: 16 December 2018

Accepted: 10 February 2019

Published: 20 October 2019

Authors

Bo Dai
School of Mathematical Sciences Peking University Beijing China

Chung-I Ho
Department of Mathematics National Kaohsiung Normal University Kaohsiung Taiwan

Tian-Jun Li
Department of Mathematics University of Minnesota Minneapolis, MN United States

Volume 19, issue 6 (2019)