Orientable hyperbolic 4-manifolds over the 120-Cell

Jiming Ma; Fangting Zheng

doi:10.1090/mcom/3625

Orientable hyperbolic 4-manifolds over the 120-Cell

Jiming Ma, Fangting Zheng^*

^*Corresponding author for this work

Department of Pure Mathematics

Fudan University

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

4 Citations (Scopus)

Abstract

Since there is no hyperbolic Dehn filling theorem for higher dimensions, it is challenging to construct explicit hyperbolic manifolds of small volume in dimension at least four. Here, we build up closed hyperbolic 4-manifolds of volume (formula presented) · 16 by using the small cover theory. In particular, we classify all of the orientable four-dimensional small covers over the rightangled 120-cell up to homeomorphism; these are all with even intersection forms.

Original language	English
Pages (from-to)	2463-2501
Number of pages	39
Journal	Mathematics of Computation
Volume	90
Issue number	331
DOIs	https://doi.org/10.1090/mcom/3625
Publication status	Published - Sept 2021

Keywords

120-Cell
hyperbolic 4-manifolds
intersection form
small cover

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10.1090/mcom/3625

Cite this

Ma, J., & Zheng, F. (2021). Orientable hyperbolic 4-manifolds over the 120-Cell. Mathematics of Computation, 90(331), 2463-2501. https://doi.org/10.1090/mcom/3625

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title = "Orientable hyperbolic 4-manifolds over the 120-Cell",

abstract = "Since there is no hyperbolic Dehn filling theorem for higher dimensions, it is challenging to construct explicit hyperbolic manifolds of small volume in dimension at least four. Here, we build up closed hyperbolic 4-manifolds of volume (formula presented) · 16 by using the small cover theory. In particular, we classify all of the orientable four-dimensional small covers over the rightangled 120-cell up to homeomorphism; these are all with even intersection forms.",

keywords = "120-Cell, hyperbolic 4-manifolds, intersection form, small cover",

author = "Jiming Ma and Fangting Zheng",

note = "Funding Information: Received by the editor March 26, 2020, and, in revised form, September 19, 2020, November 28, 2020, and December 17, 2020. 2020 Mathematics Subject Classification. Primary 32Q45, 52B70. Key words and phrases. 120-Cell, intersection form, hyperbolic 4-manifolds, small cover. The first author was partially supported by NSFC 11371094 and 11771088. The second author was supported by XJTLU Research Development Fund RDF-19-01-29. The second author is the corresponding author. Publisher Copyright: {\textcopyright} 2021 American Mathematical Society",

year = "2021",

month = sep,

doi = "10.1090/mcom/3625",

language = "English",

volume = "90",

pages = "2463--2501",

journal = "Mathematics of Computation",

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N1 - Funding Information: Received by the editor March 26, 2020, and, in revised form, September 19, 2020, November 28, 2020, and December 17, 2020. 2020 Mathematics Subject Classification. Primary 32Q45, 52B70. Key words and phrases. 120-Cell, intersection form, hyperbolic 4-manifolds, small cover. The first author was partially supported by NSFC 11371094 and 11771088. The second author was supported by XJTLU Research Development Fund RDF-19-01-29. The second author is the corresponding author. Publisher Copyright: © 2021 American Mathematical Society

PY - 2021/9

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N2 - Since there is no hyperbolic Dehn filling theorem for higher dimensions, it is challenging to construct explicit hyperbolic manifolds of small volume in dimension at least four. Here, we build up closed hyperbolic 4-manifolds of volume (formula presented) · 16 by using the small cover theory. In particular, we classify all of the orientable four-dimensional small covers over the rightangled 120-cell up to homeomorphism; these are all with even intersection forms.

AB - Since there is no hyperbolic Dehn filling theorem for higher dimensions, it is challenging to construct explicit hyperbolic manifolds of small volume in dimension at least four. Here, we build up closed hyperbolic 4-manifolds of volume (formula presented) · 16 by using the small cover theory. In particular, we classify all of the orientable four-dimensional small covers over the rightangled 120-cell up to homeomorphism; these are all with even intersection forms.

KW - 120-Cell

KW - hyperbolic 4-manifolds

KW - intersection form

KW - small cover

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SP - 2463

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JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 331

ER -

Orientable hyperbolic 4-manifolds over the 120-Cell

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Keywords

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