Algebraic & Geometric Topology

Nonorientable Lagrangian surfaces in rational $4$–manifolds

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

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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.

Article information

Source
Algebr. Geom. Topol., Volume 19, Number 6 (2019), 2837-2854.

Dates
Received: 25 August 2017
Revised: 16 December 2018
Accepted: 10 February 2019
First available in Project Euclid: 29 October 2019

Permanent link to this document
https://projecteuclid.org/euclid.agt/1572314543

Digital Object Identifier
doi:10.2140/agt.2019.19.2837

Mathematical Reviews number (MathSciNet)
MR4023330

Zentralblatt MATH identifier
07142620

Subjects
Primary: 53D12: Lagrangian submanifolds; Maslov index 57Q35: Embeddings and immersions

Keywords
nonorientable Lagrangian surface Lagrangian blowup

Citation

Dai, Bo; Ho, Chung-I; Li, Tian-Jun. Nonorientable Lagrangian surfaces in rational $4$–manifolds. Algebr. Geom. Topol. 19 (2019), no. 6, 2837--2854. doi:10.2140/agt.2019.19.2837. https://projecteuclid.org/euclid.agt/1572314543


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