TRANSCENDENTAL SIMPLICIAL VOLUMES

被引：1
作者：
Heuer, Nicolaus [1 ]
Loeh, Clara [2 ]
机构：
[1] Univ Cambridge, DPMMS, Cambridge, England
[2] Univ Regensburg, Fak Math, Regensburg, Germany
来源：
ANNALES DE L INSTITUT FOURIER | 2024年 / 74卷 / 02期
关键词：
simplicial volume; stable commutator length; right-computable numbers; STABLE COMMUTATOR LENGTH; LINEAR-FORMS; LOGARITHMS; MANIFOLDS; HOMOLOGY;
D O I：
10.5802/aif.3597
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that there exist closed manifolds with arbitrarily small transcendental simplicial volumes. Moreover, we exhibit an explicit family of (transcendental) real numbers that are not realised as the simplicial volume of a closed manifold.
引用
收藏
页码：763 / 781
页数：20
相关论文
共 39 条
  • [1] Adem Alejandro, 1998, London Math. Soc. Lecture Note Ser., V252, P1
  • [2] [Anonymous], 1980, Computability, An Introduction to Recursive Function Theory
  • [3] LINEAR FORMS IN LOGARITHMS OF ALGEBRAIC NUMBERS (3)
    BAKER, A
    [J]. MATHEMATIKA, 1967, 14 (28P2) : 220 - &
  • [4] LINEAR FORMS IN LOGARITHMS OF ALGEBRAIC NUMBERS (2)
    BAKER, A
    [J]. MATHEMATIKA, 1967, 14 (27P1) : 102 - &
  • [5] LINEAR FORMS IN LOGARITHMS OF ALGEBRAIC NUMBERS
    BAKER, A
    [J]. MATHEMATIKA, 1966, 13 (26P2) : 204 - &
  • [6] Bavard C., 1991, ENSEIGN MATH, V37, P109
  • [7] Besicovitch A.S., 1940, J LOND MATH SOC, V15, P3, DOI DOI 10.1112/JLMS/S1-15.1.3
  • [8] Brown K. S., 1994, Graduate Texts in Mathematics, V87, DOI [10.1007/978-1-4684-9327-6, DOI 10.1007/978-1-4684-9327-6]
  • [9] The Bounded Cohomology of SL2 Over Local Fields and S-Integers
    Bucher, Michelle
    Monod, Nicolas
    [J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2019, 2019 (06) : 1601 - 1611
  • [10] A note on semi-conjugacy for circle actions
    Bucher, Michelle
    Frigerio, Roberto
    Hartnick, Tobias
    [J]. ENSEIGNEMENT MATHEMATIQUE, 2016, 62 (3-4): : 317 - 360
1234