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Free actions of finite abelian groups on 3-dimensional nilmanifolds

신준국|최동순
대한수학회 (The Korean Mathematical Society)|2005.07|대한수학회지 (Journal of the KMS)|제42권 제4호|pp. 795-826

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Abstract

We study free actions of finite abelian groups on3-dimensional nilmanifolds. By the works of Bieberbach andWaldhausen, this classification problem is reduced to classifyingall normal nilpotent subgroups of almost Bieberbach groups offinite index, up to affine conjugacy. All such actions arecompletely classified.

참고문헌 (12)

  1. "Shin \paper Free actions offinite groups on the 3-dimensional nilmanifold", 144, pp.255~270
  2. "Lee\paper Affine structures for closed 3-dimensional manifolds withnil-geometry \yr1995 \vol 46 \jour Quart", pp.141~67
  3. "Lee\paper Classification of free actions of finite groups on the$3$", 121(3), pp.469~507
  4. "Heil \paper On $P^2$-irreducible $3$-manifolds\jour Bull", 75 \yr 1969 \pages772--775
  5. "Hempel \paper Free cyclic actions of $S^1\timesS^1\times S^1$ \jour Proc", pp.221~
  6. "Lee \pages 61--66 \paper There are onlyfinitely many infra-nilmanifolds under each manifold \yr 1988 \vol39 \jour Quart"
  7. "Raymond \paper Rigidity of almostcrystallographic groups \yr1985 \vol 44 \page 73--78 \jourContemp"
  8. "Shoji \paper Freeactions of finite abelian groups on the 3-Torus \jour TopologyAppl"
  9. "Orlik \paper Seifert Manifolds \jour LectureNotes in Math" (1972), \vol 291 \publ Springer-Verlag
  10. "Scott \paper The geometries of 3-manifolds\yr1983 \vol 15 \pages 401--489 \jour Bull"
  11. "Shin \paper Isometry groups of unimodularsimply connected 3-dimensional Lie groups \", 65, pp.267~290
  12. "Waldhausen \paper On irreducible $3$-manifoldswhich are sufficiently large \jour Ann"

관련 논문AI추천

CLASSIFICATION OF FREE ACTIONS OF FINITE GROUPS ON 3-DIMENSIONAL NILMANIFOLDS구대환, 신준국, 오명성대한수학회 · 대한수학회지2017 · 제54권 제5호Deformation spaces of 3-dimensional flat manifoldsEun Sook Kang, Ju Young Kim대한수학회 · 대한수학회논문집2003 · 제18권 제1호Geometric Group Actions on Lens SpacesAndy Miller, John Kalliongis경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2002 · 제42권 제2호Moduli Spaces of 3-dimensional Flat Manifolds강은숙대한수학회 · 대한수학회지2006 · 제43권 제5호Corrigendum to ``Free actions of finite abelian groups on 3-dimensional nilmanifolds'' [J. Korean Math. Soc. 42 (2005), No. 4, pp. 795--826]신준국, 최동순대한수학회 · 대한수학회지2019 · 제56권 제1호Automorphisms of uniform lattices of nilpotent Lie groups up to dimension four이상래, 이종범대한수학회 · 대한수학회논문집2020 · 제35권 제2호

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