본문 바로가기
KERD
논문KCI 등재

CLASSIFICATION OF FREE ACTIONS OF FINITE GROUPS ON 3-DIMENSIONAL NILMANIFOLDS

신준국|구대환|오명성
대한수학회 (The Korean Mathematical Society)|2017.09|대한수학회지 (Journal of the KMS)|제54권 제5호|pp. 1411-1440

1

조회

0

다운로드

3

인용

0

참고문헌

키워드

group actionHeisenberg groupaffine conjugacyalmost Bieberbach group
주제분류수학

초록

We study free actions of finite groups on 3-dimensional nilmanifolds with the first homology $\bz^2\oplus \bz_p$. By the works of Bieberbach and Waldhausen, this classification problem is reduced to classifying all normal nilpotent subgroups of almost Bieberbach groups of finite index, up to affine conjugacy.

Abstract

We study free actions of finite groups on 3-dimensional nilmanifolds with the first homology $\bz^2\oplus \bz_p$. By the works of Bieberbach and Waldhausen, this classification problem is reduced to classifying all normal nilpotent subgroups of almost Bieberbach groups of finite index, up to affine conjugacy.

참고문헌 (17)

  1. 최동순, "Free actions of finite abelian groups on 3-dimensional nilmanifolds", 대한수학회지, 42(4), pp.795~826 (2005), 대한수학회
  2. H. Y. Chu, "Free actions of finite groups on the 3-dimensional nilmanifold", Topology Appl, 144(1-3), pp.255~270 (2004)
  3. K. Dekimpe, "Affine structures for closed 3-dimensional manifolds with nil-geometry", Quart. J. Math. Oxford Ser. (2), 46(182), pp.141~167 (1995)
  4. K. Y. Ha, "Classification of free actions of finite groups on the 3-torus", Topology Appl, 121(3), pp.469~507 (2002)
  5. W. Heil, "On P2-irreducible 3-manifolds", Bull. Amer. Math. Soc, 75, pp.772~775 (1969)
  6. W. Heil, "Almost sufficiently large Seifert fiber spaces", Michigan Math. J, 20, pp.217~223 (1973)
  7. J. Hempel, "Free cyclic actions of S1 × S1 × S1", Proc. Amer. Math. Soc, 48(1), pp.221~227 (1975)
  8. K. B. Lee, "There are only finitely many infra-nilmanifolds under each manifold", Quart. J. Math. Oxford Ser. (2), 39(153), pp.61~66 (1988)
  9. K. B. Lee, "Combinatorial methods in topology and algebraic geometry", pp.73~78 (1985), Amer. Math. Soc
  10. K. B. Lee, "Free actions of finite abelian groups on the 3-torus", Topology Appl, 53(2), pp.153~175 (1993)
  11. Myung Sung Oh, "Free actions on the 3-dimensional nilmanifold", 충청수학회지, 20(3), pp.223~230 (2007), 충청수학회
  12. P. Orlik, "Seifert Manifolds" (1972), Springer-Verlag
  13. P. Scott, "The geometries of 3-manifolds", Bull. London Math. Soc, 15(5), pp.401~487 (1983)
  14. J. K. Shin, "Isometry groups of unimodular simply connected 3-dimensional Lie groups", Geom. Dedicata, 65(3), pp.267~290 (1997)
  15. 신준국, "Free actions of finite groups on the 3-dimensional nilmanifold for Type 1", 충청수학회지, 19(4), pp.437~443 (2006), 충청수학회
  16. F. Waldhausen, "On irreducible 3-manifolds which are sufficiently large", Ann. of Math, 87(2), pp.56~88 (1968)
  17. S. Wolfram, "Mathematica" (1993), Wolfram Research

관련 논문AI추천

Free actions of finite abelian groups on 3-dimensional nilmanifolds신준국, 최동순대한수학회 · 대한수학회지2005 · 제42권 제4호Automorphisms of uniform lattices of nilpotent Lie groups up to dimension four이상래, 이종범대한수학회 · 대한수학회논문집2020 · 제35권 제2호Nielsen spectrum of maps on infra-solvmanifolds modeled on Sol0⁴이종범대한수학회 · 대한수학회보2020 · 제57권 제4호Algebraic ranks of the fundamental groups of high dimensional graph manifolds김래용대한수학회 · 대한수학회보2021 · 제58권 제2호On the actions of Higman-Thompson groups by homeomorphisms김진홍대한수학회 · 대한수학회보2020 · 제57권 제2호Equivalence of Cyclic p-squared Actions on HandlebodiesJesse Prince-Lubawy경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2018 · 제58권 제3호

이 간행물의 다른 논문 (13건)

GLOBAL Wp1,2 ESTIMATES FOR NONDIVERGENCE PARABOLIC OPERATORS WITH POTENTIALS SATISFYING A REVERSE HOLDER CONDITIONLin Tang, Guixia Panpp. 1357-1377HILBERT FUNCTIONS OF STANDARD k-ALGEBRAS DEFINED BY SKEW-SYMMETRIZABLE MATRICES강오진pp. 1379-1410ALMOST EINSTEIN MANIFOLDS WITH CIRCULANT STRUCTURESIva Dokuzovapp. 1441-1456FOXBY EQUIVALENCE RELATIVE TO C-WEAK INJECTIVE AND C-WEAK FLAT MODULESTiwei Zhao, Zenghui Gaopp. 1457-1482THE NAVIER-STOKES EQUATIONS WITH INITIAL VALUES IN BESOV SPACES OF TYPE B-1q,∞+3/qPen-Yuan Hsu, Reinhard Farwig, Yoshikazu Gigapp. 1483-1504
원문 보기