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ALEXANDER r-TUPLES AND BIER COMPLEXES. / Jojic, Dusko; Некрасов, Илья Игоревич; Панина, Гаянэ Юрьевна; Zivaljevic, Rade.

In: Publications de l'Institut Mathematique, Vol. 104, No. 118, 2018, p. 1-22.

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

Harvard

Jojic, D, Некрасов, ИИ, Панина, ГЮ & Zivaljevic, R 2018, 'ALEXANDER r-TUPLES AND BIER COMPLEXES', Publications de l'Institut Mathematique, vol. 104, no. 118, pp. 1-22. https://doi.org/10.2298/PIM1818001J

APA

Jojic, D., Некрасов, И. И., Панина, Г. Ю., & Zivaljevic, R. (2018). ALEXANDER r-TUPLES AND BIER COMPLEXES. Publications de l'Institut Mathematique, 104(118), 1-22. https://doi.org/10.2298/PIM1818001J

Vancouver

Jojic D, Некрасов ИИ, Панина ГЮ, Zivaljevic R. ALEXANDER r-TUPLES AND BIER COMPLEXES. Publications de l'Institut Mathematique. 2018;104(118):1-22. https://doi.org/10.2298/PIM1818001J

Author

Jojic, Dusko ; Некрасов, Илья Игоревич ; Панина, Гаянэ Юрьевна ; Zivaljevic, Rade. / ALEXANDER r-TUPLES AND BIER COMPLEXES. In: Publications de l'Institut Mathematique. 2018 ; Vol. 104, No. 118. pp. 1-22.

BibTeX

@article{53dbd7a072884daca52d4556aa2fab5e,
title = "ALEXANDER r-TUPLES AND BIER COMPLEXES",
abstract = "We introduce and study Alexander r-tuples K = <K-i >(r)(i=1) of simplicial complexes, as a common generalization of pairs of Alexander dual complexes (Alexander 2-tuples) and r-unavoidable complexes of [3] and [11]. In the same vein, the Bier complexes, defined as the deleted joins K-Delta*of Alexander r-tuples, include both standard Bier spheres and optimal multiple chessboard complexes (Section 2.2) as interesting, special cases.Our main results are Theorem 4.1 saying that (1) the r-fold deleted join of Alexander r-tuple is a pure complex homotopy equivalent to a wedge of spheres, and (2) the r-fold deleted join of a collective unavoidable r-tuple is (n - r - 1)-connected, and a classification theorem (Theorem 5.1 and Corollary 5.1) for Alexander r-tuples and Bier complexes.",
keywords = "Двойственность Александера, дискретная теория Морса, Бировы сферы, Bier spheres, Alexander duality, chessboard complexes, unavoidable complexes, discrete Morse theory, SPHERES",
author = "Dusko Jojic and Некрасов, {Илья Игоревич} and Панина, {Гаянэ Юрьевна} and Rade Zivaljevic",
year = "2018",
doi = "10.2298/PIM1818001J",
language = "English",
volume = "104",
pages = "1--22",
journal = "Publications de l'Institut Mathematique",
issn = "0350-1302",
publisher = "Mathematical Institute of the Serbian Academy of Sciences and Arts",
number = "118",

}

RIS

TY - JOUR

T1 - ALEXANDER r-TUPLES AND BIER COMPLEXES

AU - Jojic, Dusko

AU - Некрасов, Илья Игоревич

AU - Панина, Гаянэ Юрьевна

AU - Zivaljevic, Rade

PY - 2018

Y1 - 2018

N2 - We introduce and study Alexander r-tuples K = <K-i >(r)(i=1) of simplicial complexes, as a common generalization of pairs of Alexander dual complexes (Alexander 2-tuples) and r-unavoidable complexes of [3] and [11]. In the same vein, the Bier complexes, defined as the deleted joins K-Delta*of Alexander r-tuples, include both standard Bier spheres and optimal multiple chessboard complexes (Section 2.2) as interesting, special cases.Our main results are Theorem 4.1 saying that (1) the r-fold deleted join of Alexander r-tuple is a pure complex homotopy equivalent to a wedge of spheres, and (2) the r-fold deleted join of a collective unavoidable r-tuple is (n - r - 1)-connected, and a classification theorem (Theorem 5.1 and Corollary 5.1) for Alexander r-tuples and Bier complexes.

AB - We introduce and study Alexander r-tuples K = <K-i >(r)(i=1) of simplicial complexes, as a common generalization of pairs of Alexander dual complexes (Alexander 2-tuples) and r-unavoidable complexes of [3] and [11]. In the same vein, the Bier complexes, defined as the deleted joins K-Delta*of Alexander r-tuples, include both standard Bier spheres and optimal multiple chessboard complexes (Section 2.2) as interesting, special cases.Our main results are Theorem 4.1 saying that (1) the r-fold deleted join of Alexander r-tuple is a pure complex homotopy equivalent to a wedge of spheres, and (2) the r-fold deleted join of a collective unavoidable r-tuple is (n - r - 1)-connected, and a classification theorem (Theorem 5.1 and Corollary 5.1) for Alexander r-tuples and Bier complexes.

KW - Двойственность Александера, дискретная теория Морса, Бировы сферы

KW - Bier spheres

KW - Alexander duality

KW - chessboard complexes

KW - unavoidable complexes

KW - discrete Morse theory

KW - SPHERES

U2 - 10.2298/PIM1818001J

DO - 10.2298/PIM1818001J

M3 - Article

VL - 104

SP - 1

EP - 22

JO - Publications de l'Institut Mathematique

JF - Publications de l'Institut Mathematique

SN - 0350-1302

IS - 118

ER -

ID: 34839118