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

1 Scopus citations

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

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© 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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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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Nonorientable Lagrangian surfaces in rational 4-manifolds

Abstract

Bibliographical note

Keywords

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