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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
Abstract

We show that for any nonzero class A in H2(X; 2) in a rational 4manifold X, A is represented by a nonorientable embedded Lagrangian surface L (for some symplectic structure) if and only if P(A) χ(L)(mod4), where P(A) denotes the mod 4 valued Pontryagin square of A.

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