Nonorientable Lagrangian surfaces in rational 4-manifolds

Bo Dai; Chung I. Ho; Tian Jun Li

doi:10.2140/agt.2019.19.2837

Nonorientable Lagrangian surfaces in rational 4-manifolds

Bo Dai, Chung I. Ho, Tian Jun Li

Mathematics

Research output: Contribution to journal › Article › peer-review

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Abstract

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 language	English (US)
Pages (from-to)	2837-2854
Number of pages	18
Journal	Algebraic and Geometric Topology
Volume	19
Issue number	6
DOIs	https://doi.org/10.2140/agt.2019.19.2837
State	Published - 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.

Keywords

Lagrangian blowup
Nonorientable Lagrangian surface

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title = "Nonorientable Lagrangian surfaces in rational 4-manifolds",

abstract = "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.",

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year = "2019",

doi = "10.2140/agt.2019.19.2837",

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T1 - Nonorientable Lagrangian surfaces in rational 4-manifolds

AU - Dai, Bo

AU - Ho, Chung I.

AU - Li, Tian Jun

N1 - 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.

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - Lagrangian blowup

KW - Nonorientable Lagrangian surface

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JO - Algebraic and Geometric Topology

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ER -

Nonorientable Lagrangian surfaces in rational 4-manifolds

Abstract

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Keywords

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