The Poincaré Conjecture and related statements

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The Poincaré Conjecture and related statements. / Berestovskii, Valerii N.

Geometry in History. Springer International Publishing AG, 2019. p. 623-685.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Research › peer-review

Harvard

Berestovskii, VN 2019, The Poincaré Conjecture and related statements. in Geometry in History. Springer International Publishing AG, pp. 623-685. https://doi.org/10.1007/978-3-030-13609-3_17

APA

Berestovskii, V. N. (2019). The Poincaré Conjecture and related statements. In Geometry in History (pp. 623-685). Springer International Publishing AG. https://doi.org/10.1007/978-3-030-13609-3_17

Vancouver

Berestovskii VN. The Poincaré Conjecture and related statements. In Geometry in History. Springer International Publishing AG. 2019. p. 623-685 doi: 10.1007/978-3-030-13609-3_17

Author

Berestovskii, Valerii N. / The Poincaré Conjecture and related statements. Geometry in History. Springer International Publishing AG, 2019. pp. 623-685

BibTeX

@inbook{91c231cd38564cdb83ea23b7631fddbd,

title = "The Poincar{\'e} Conjecture and related statements",

abstract = "The main topics of this paper are mathematical statements, results or problems related with the Poincar{\'e} conjecture, a recipe to recognize the threedimensional sphere. The statements, results and problems are equivalent forms, corollaries, strengthenings of this conjecture, or problems of a more general nature such as the homeomorphism problem, the manifold recognition problem and the existence problem of some polyhedral, smooth and geometric structures on topological manifolds. Examples of polyhedral structures are simplicial triangulations and combinatorial simplicial triangulations of topological manifolds; so appears the triangulation conjecture, more exactly, the triangulation problem. Examples of geometric structures are Riemannian metrics that are locally homogeneous or have constant zero, positive or negative sectional curvature; more general structures are intrinsic or geodesic metrics with curvature bounded above or/and below in the sense of A.D. Alexandrov or with nonpositive curvature in the sense of H. Busemann.",

author = "Berestovskii, {Valerii N.}",

year = "2019",

month = oct,

day = "18",

doi = "10.1007/978-3-030-13609-3_17",

language = "English",

isbn = "9783030136086",

pages = "623--685",

booktitle = "Geometry in History",

publisher = "Springer International Publishing AG",

address = "Switzerland",

}

RIS

TY - CHAP

T1 - The Poincaré Conjecture and related statements

AU - Berestovskii, Valerii N.

PY - 2019/10/18

Y1 - 2019/10/18

N2 - The main topics of this paper are mathematical statements, results or problems related with the Poincaré conjecture, a recipe to recognize the threedimensional sphere. The statements, results and problems are equivalent forms, corollaries, strengthenings of this conjecture, or problems of a more general nature such as the homeomorphism problem, the manifold recognition problem and the existence problem of some polyhedral, smooth and geometric structures on topological manifolds. Examples of polyhedral structures are simplicial triangulations and combinatorial simplicial triangulations of topological manifolds; so appears the triangulation conjecture, more exactly, the triangulation problem. Examples of geometric structures are Riemannian metrics that are locally homogeneous or have constant zero, positive or negative sectional curvature; more general structures are intrinsic or geodesic metrics with curvature bounded above or/and below in the sense of A.D. Alexandrov or with nonpositive curvature in the sense of H. Busemann.

AB - The main topics of this paper are mathematical statements, results or problems related with the Poincaré conjecture, a recipe to recognize the threedimensional sphere. The statements, results and problems are equivalent forms, corollaries, strengthenings of this conjecture, or problems of a more general nature such as the homeomorphism problem, the manifold recognition problem and the existence problem of some polyhedral, smooth and geometric structures on topological manifolds. Examples of polyhedral structures are simplicial triangulations and combinatorial simplicial triangulations of topological manifolds; so appears the triangulation conjecture, more exactly, the triangulation problem. Examples of geometric structures are Riemannian metrics that are locally homogeneous or have constant zero, positive or negative sectional curvature; more general structures are intrinsic or geodesic metrics with curvature bounded above or/and below in the sense of A.D. Alexandrov or with nonpositive curvature in the sense of H. Busemann.

UR - http://www.scopus.com/inward/record.url?scp=85084327170&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-13609-3_17

DO - 10.1007/978-3-030-13609-3_17

M3 - Chapter

AN - SCOPUS:85084327170

SN - 9783030136086

SP - 623

EP - 685

BT - Geometry in History

PB - Springer International Publishing AG

ER -

ID: 35676973