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

School of 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

Bibliographical note

Publisher Copyright:
© 2019, Mathematical Sciences Publishers. All rights reserved.

Keywords

Lagrangian blowup
Nonorientable Lagrangian surface

Publisher link

10.2140/agt.2019.19.2837

Find It

Find It at U of M Libraries

Cite this

@article{e0b4a3a40e9946e8a119ca1aa88b3890,

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.",

keywords = "Lagrangian blowup, Nonorientable Lagrangian surface",

author = "Bo Dai and Ho, {Chung I.} and Li, {Tian Jun}",

year = "2019",

doi = "10.2140/agt.2019.19.2837",

language = "English (US)",

volume = "19",

pages = "2837--2854",

journal = "Algebraic and Geometric Topology",

issn = "1472-2747",

publisher = "Mathematical Sciences Publishers",

number = "6",

}

TY - JOUR

T1 - Nonorientable Lagrangian surfaces in rational 4-manifolds

AU - Dai, Bo

AU - Ho, Chung I.

AU - Li, Tian Jun

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

UR - http://www.scopus.com/inward/record.url?scp=85074368059&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85074368059&partnerID=8YFLogxK

U2 - 10.2140/agt.2019.19.2837

DO - 10.2140/agt.2019.19.2837

M3 - Article

AN - SCOPUS:85074368059

SN - 1472-2747

VL - 19

SP - 2837

EP - 2854

JO - Algebraic and Geometric Topology

JF - Algebraic and Geometric Topology

IS - 6

ER -

Nonorientable Lagrangian surfaces in rational 4-manifolds

Abstract

Bibliographical note

Keywords

Publisher link

Find It

Other files and links

Fingerprint

Cite this