On Flag-No-Square 4-Manifolds

Daniel Kalmanovich; Eran Nevo; Gangotryi Sorcar

doi:10.1007/s00454-025-00774-x

On Flag-No-Square 4-Manifolds

Daniel Kalmanovich^*
, Eran Nevo
, Gangotryi Sorcar

^*Corresponding author for this work

Einstein Institute of Mathematics

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

Abstract

Which 4-manifolds admit a flag-no-square (fns) triangulation? We introduce the “star-connected-sum" operation on such triangulations, which preserves the fns property, from which we derive new constructions of fns 4-manifolds. In particular, we show the following: (i) there exist non-aspherical fns 4-manifolds, answering in the negative a question by Przytycki and Swiatkowski; (ii) for every large enough integer k there exists a fns 4-manifold M2k of Euler characteristic 2k, and further, (iii) M2k admits a super-exponential number (in k) of fns triangulations - at least 2Ω(klogk) and at most 2O(k1.5logk).

Original language	English
Journal	Discrete and Computational Geometry
DOIs	https://doi.org/10.1007/s00454-025-00774-x
State	Accepted/In press - 2025

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.

Keywords

4-manifold
Connected sum
Euler characteristic
Flag-no-square triangulation

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10.1007/s00454-025-00774-x

Cite this

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abstract = "Which 4-manifolds admit a flag-no-square (fns) triangulation? We introduce the “star-connected-sum{"} operation on such triangulations, which preserves the fns property, from which we derive new constructions of fns 4-manifolds. In particular, we show the following: (i) there exist non-aspherical fns 4-manifolds, answering in the negative a question by Przytycki and Swiatkowski; (ii) for every large enough integer k there exists a fns 4-manifold M2k of Euler characteristic 2k, and further, (iii) M2k admits a super-exponential number (in k) of fns triangulations - at least 2Ω(klogk) and at most 2O(k1.5logk).",

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AU - Kalmanovich, Daniel

AU - Nevo, Eran

AU - Sorcar, Gangotryi

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.

PY - 2025

Y1 - 2025

N2 - Which 4-manifolds admit a flag-no-square (fns) triangulation? We introduce the “star-connected-sum" operation on such triangulations, which preserves the fns property, from which we derive new constructions of fns 4-manifolds. In particular, we show the following: (i) there exist non-aspherical fns 4-manifolds, answering in the negative a question by Przytycki and Swiatkowski; (ii) for every large enough integer k there exists a fns 4-manifold M2k of Euler characteristic 2k, and further, (iii) M2k admits a super-exponential number (in k) of fns triangulations - at least 2Ω(klogk) and at most 2O(k1.5logk).

AB - Which 4-manifolds admit a flag-no-square (fns) triangulation? We introduce the “star-connected-sum" operation on such triangulations, which preserves the fns property, from which we derive new constructions of fns 4-manifolds. In particular, we show the following: (i) there exist non-aspherical fns 4-manifolds, answering in the negative a question by Przytycki and Swiatkowski; (ii) for every large enough integer k there exists a fns 4-manifold M2k of Euler characteristic 2k, and further, (iii) M2k admits a super-exponential number (in k) of fns triangulations - at least 2Ω(klogk) and at most 2O(k1.5logk).

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KW - Connected sum

KW - Euler characteristic

KW - Flag-no-square triangulation

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On Flag-No-Square 4-Manifolds

Abstract

Bibliographical note

Keywords

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