论文信息 - Computational Aspects of Group Extensions and Their Applications in Topology

Computational Aspects of Group Extensions and Their Applications in Topology

We describe algorithms to determine extensions of infinite polycyclic groups having certain properties. In particular, we are interested in torsion-free extensions and extensions whose Fitting subgroup has a minimal centre. Then we apply these methods in topological applications. We discuss the calculation of Betti numbers for compact manifolds, and we describe algorithmic approaches in classifying almost Bieberbach groups.

Bettina Eick | Karel Dekimpe

[1] Paul G. Igodt,et al. Polycyclic–by–finite groups admit a bounded-degree polynomial structure , 1997 .

[2] Bettina Eick. Computing with infinite polycyclic groups , 2001 .

[3] Aaas News,et al. Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[4] T. Hahn. International tables for crystallography , 2002 .

[5] Charles C. Sims,et al. Computation with finitely presented groups , 1994, Encyclopedia of mathematics and its applications.

[6] Michel Goze,et al. Nilpotent Lie Algebras , 1996 .

[7] Kyung Bai Lee,et al. Maximal Holonomy of Almost Bieberbach Groups for Heis5 , 2001 .

[8] P. E. Conner,et al. Deforming homotopy equivalences to homeomorphisms in aspherical manifolds , 1977 .

[9] Kenneth S. Brown,et al. Cohomology of Groups , 1982 .

[10] J. Humphreys. A Course in Group Theory , 1996 .

[11] Bettina Eick,et al. Groups St Andrews 2001 in Oxford: Computations with almost-crystallographic groups , 2003 .

[12] H. Brown,et al. Crystallographic Groups of Four-Dimensional Space , 1978 .

[13] B. Eick,et al. Algorithms for Polycyclic Groups , 2000 .

[14] Kyung Bai Lee. THERE ARE ONLY FINITELY MANY INFRA-NILMANIFOLDS UNDER EACH NILMANIFOLD , 1988 .

[15] Paul G. Igodt,et al. AFFINE STRUCTURES FOR CLOSED 3-DIMENSIONAL MANIFOLDS WITH NIL-GEOMETRY , 1995 .

[16] Karel Dekimpe,et al. Almost-Bieberbach Groups: Affine and Polynomial Structures , 1996 .