Homeomorphic arrangements of smooth manifolds

Eran Liberman; Mina Teicher

doi:10.3390/sym13060981

Homeomorphic arrangements of smooth manifolds

Eran Liberman, Mina Teicher

Department of Mathematics

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

1 Scopus citations

Abstract

Symmetry between mathematical constructions is a very desired phenomena in mathematics in general, and in algebraic geometry in particular. For line arrangements, symmetry between topological characterizations and the combinatorics of the arrangement has often been studied, and the first counterexample where symmetry breaks is in dimension 13. In the first part of this paper, we shall prove that two arrangements of smooth compact manifolds of any dimension that are connected through smooth functions are homeomorphic. In the second part, we prove this in the affine case in dimension 4.

Original language	English
Article number	981
Journal	Symmetry
Volume	13
Issue number	6
DOIs	https://doi.org/10.3390/sym13060981
State	Published - Jun 2021

Bibliographical note

Funding Information:
Funding: This research was supported by the ISF-NSFC joint research program (grant No. 3210/19).

Publisher Copyright:
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.

Keywords

Homeomorphism
Lines
Smooth manifold

Access to Document

10.3390/sym13060981

Cite this

@article{b9913265b2714637be6df3229ce0cfc9,

title = "Homeomorphic arrangements of smooth manifolds",

abstract = "Symmetry between mathematical constructions is a very desired phenomena in mathematics in general, and in algebraic geometry in particular. For line arrangements, symmetry between topological characterizations and the combinatorics of the arrangement has often been studied, and the first counterexample where symmetry breaks is in dimension 13. In the first part of this paper, we shall prove that two arrangements of smooth compact manifolds of any dimension that are connected through smooth functions are homeomorphic. In the second part, we prove this in the affine case in dimension 4.",

keywords = "Homeomorphism, Lines, Smooth manifold",

author = "Eran Liberman and Mina Teicher",

note = "Publisher Copyright: {\textcopyright} 2021 by the authors. Licensee MDPI, Basel, Switzerland.",

year = "2021",

month = jun,

doi = "10.3390/sym13060981",

language = "אנגלית",

volume = "13",

journal = "Symmetry",

issn = "2073-8994",

publisher = "MDPI Multidisciplinary Digital Publishing Institute",

number = "6",

}

TY - JOUR

T1 - Homeomorphic arrangements of smooth manifolds

AU - Liberman, Eran

AU - Teicher, Mina

PY - 2021/6

Y1 - 2021/6

N2 - Symmetry between mathematical constructions is a very desired phenomena in mathematics in general, and in algebraic geometry in particular. For line arrangements, symmetry between topological characterizations and the combinatorics of the arrangement has often been studied, and the first counterexample where symmetry breaks is in dimension 13. In the first part of this paper, we shall prove that two arrangements of smooth compact manifolds of any dimension that are connected through smooth functions are homeomorphic. In the second part, we prove this in the affine case in dimension 4.

AB - Symmetry between mathematical constructions is a very desired phenomena in mathematics in general, and in algebraic geometry in particular. For line arrangements, symmetry between topological characterizations and the combinatorics of the arrangement has often been studied, and the first counterexample where symmetry breaks is in dimension 13. In the first part of this paper, we shall prove that two arrangements of smooth compact manifolds of any dimension that are connected through smooth functions are homeomorphic. In the second part, we prove this in the affine case in dimension 4.

KW - Homeomorphism

KW - Lines

KW - Smooth manifold

UR - http://www.scopus.com/inward/record.url?scp=85107987318&partnerID=8YFLogxK

U2 - 10.3390/sym13060981

DO - 10.3390/sym13060981

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85107987318

SN - 2073-8994

VL - 13

JO - Symmetry

JF - Symmetry

IS - 6

M1 - 981

ER -

Homeomorphic arrangements of smooth manifolds

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this