Any oriented non-closed connected 4-manifold can be spread holomorphically over the complex projective plane minus a point

Dennis Sullivan

doi:10.4310/PAMQ.2023.v19.n6.a11

Any oriented non-closed connected 4-manifold can be spread holomorphically over the complex projective plane minus a point

Dennis Sullivan

Mathematics

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

Abstract

We give a 1965 era proof of the title assuming M is spin^c. The fact that any oriented four manifold is spin^c is a challenging result from 1995 whose interesting argument by Teichner-Vogt is analyzed and used in the appendix to show an analogous integral lift result about the top Wu class in dim 4k. This will be used in future work to study related complex structures on higher dimensional open manifolds.

Original language	English
Pages (from-to)	2915-2918
Number of pages	4
Journal	Pure and Applied Mathematics Quarterly
Volume	19
Issue number	6
DOIs	https://doi.org/10.4310/PAMQ.2023.v19.n6.a11
State	Published - 2023

Keywords

4-manifolds
complex structures
spin

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10.4310/PAMQ.2023.v19.n6.a11

Cite this

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title = "Any oriented non-closed connected 4-manifold can be spread holomorphically over the complex projective plane minus a point",

abstract = "We give a 1965 era proof of the title assuming M is spinc. The fact that any oriented four manifold is spinc is a challenging result from 1995 whose interesting argument by Teichner-Vogt is analyzed and used in the appendix to show an analogous integral lift result about the top Wu class in dim 4k. This will be used in future work to study related complex structures on higher dimensional open manifolds.",

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AB - We give a 1965 era proof of the title assuming M is spinc. The fact that any oriented four manifold is spinc is a challenging result from 1995 whose interesting argument by Teichner-Vogt is analyzed and used in the appendix to show an analogous integral lift result about the top Wu class in dim 4k. This will be used in future work to study related complex structures on higher dimensional open manifolds.

KW - 4-manifolds

KW - complex structures

KW - spin

UR - https://www.scopus.com/pages/publications/85184455367

U2 - 10.4310/PAMQ.2023.v19.n6.a11

DO - 10.4310/PAMQ.2023.v19.n6.a11

M3 - Article

AN - SCOPUS:85184455367

SN - 1558-8599

VL - 19

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JO - Pure and Applied Mathematics Quarterly

JF - Pure and Applied Mathematics Quarterly

IS - 6

ER -

Any oriented non-closed connected 4-manifold can be spread holomorphically over the complex projective plane minus a point

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