Simplified broken Lefschetz fibrations and trisections of 4-manifolds

R. Inanç Baykur, Osamu Saeki

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Shapes of 4D spaces can be studied effectively via maps to standard surfaces. We explain, and illustrate by quintessential examples, how to simplify such generic maps on 4-manifolds topologically, to derive simple decompositions into much betterunderstood manifold pieces. Our methods not only allow us to produce various interesting families of examples but also to establish a correspondence between simplified broken Lefschetz fibrations and simplified trisections of closed, oriented 4-manifolds.

Original languageEnglish
Pages (from-to)10894-10900
Number of pages7
JournalProceedings of the National Academy of Sciences of the United States of America
Volume115
Issue number43
DOIs
Publication statusPublished - Oct 23 2018

All Science Journal Classification (ASJC) codes

  • General

Cite this

Simplified broken Lefschetz fibrations and trisections of 4-manifolds. / Baykur, R. Inanç; Saeki, Osamu.

In: Proceedings of the National Academy of Sciences of the United States of America, Vol. 115, No. 43, 23.10.2018, p. 10894-10900.

Research output: Contribution to journalArticle

@article{c435f13119ea42e6bf8b7854fc7336a6,
title = "Simplified broken Lefschetz fibrations and trisections of 4-manifolds",
abstract = "Shapes of 4D spaces can be studied effectively via maps to standard surfaces. We explain, and illustrate by quintessential examples, how to simplify such generic maps on 4-manifolds topologically, to derive simple decompositions into much betterunderstood manifold pieces. Our methods not only allow us to produce various interesting families of examples but also to establish a correspondence between simplified broken Lefschetz fibrations and simplified trisections of closed, oriented 4-manifolds.",
author = "Baykur, {R. Inan{\cc}} and Osamu Saeki",
year = "2018",
month = "10",
day = "23",
doi = "10.1073/pnas.1717175115",
language = "English",
volume = "115",
pages = "10894--10900",
journal = "Proceedings of the National Academy of Sciences of the United States of America",
issn = "0027-8424",
number = "43",

}

TY - JOUR

T1 - Simplified broken Lefschetz fibrations and trisections of 4-manifolds

AU - Baykur, R. Inanç

AU - Saeki, Osamu

PY - 2018/10/23

Y1 - 2018/10/23

N2 - Shapes of 4D spaces can be studied effectively via maps to standard surfaces. We explain, and illustrate by quintessential examples, how to simplify such generic maps on 4-manifolds topologically, to derive simple decompositions into much betterunderstood manifold pieces. Our methods not only allow us to produce various interesting families of examples but also to establish a correspondence between simplified broken Lefschetz fibrations and simplified trisections of closed, oriented 4-manifolds.

AB - Shapes of 4D spaces can be studied effectively via maps to standard surfaces. We explain, and illustrate by quintessential examples, how to simplify such generic maps on 4-manifolds topologically, to derive simple decompositions into much betterunderstood manifold pieces. Our methods not only allow us to produce various interesting families of examples but also to establish a correspondence between simplified broken Lefschetz fibrations and simplified trisections of closed, oriented 4-manifolds.

UR - http://www.scopus.com/inward/record.url?scp=85055438841&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85055438841&partnerID=8YFLogxK

U2 - 10.1073/pnas.1717175115

DO - 10.1073/pnas.1717175115

M3 - Article

C2 - 30348799

AN - SCOPUS:85055438841

VL - 115

SP - 10894

EP - 10900

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

SN - 0027-8424

IS - 43

ER -