Home Newsletter
News Books
Welcome to FreeScience.info Language/Lingua

Books 3054
· Book News
· Most clicked
· Least clicked

Search for a Book
Add a new Book

Connectivity of the coset poset

Author: Daniel A. Ramras
Url: http://arxiv.org/abs/math.GR/0208176
Format: Ps,Pdf
Year: 2002
Category: Topology
Pages: 81
Clicks: 3215

Topological concepts may be applied to any poset via the simplicial complex of finite chains. The coset poset C(G) of a finite group G (consisting of all cosets of all proper subgroups of G, ordered by inclusion) was introduced by Kenneth S. Brown in his study of the probabilistic zeta function P(G,s), and Brown\'s results motivate the study of the homotopy type of C(G). After a detailed introduction to basic simplicial topology and homotopy theory for finite posets (Chapter 2), we examine the connectivity of the coset poset (Chapter 3). Of particular interest is the fundamental group, and we provide various conditions under which C(G) is or is not simply connected. In particular, we classify direct products with simply connected coset posets. In Chapter 4, we treat several specific examples, including A_5 and PSL(2,7). We prove that both of these groups have simply connected coset posets, and in fact determine the precise homotopy type of C(A_5). This chapter also includes a detailed determination of all subgroups of the groups PSL(2,p), p prime (following Burnside). The final chapter discusses conjectures and directions for further research.

Similar Books
Topology Course Lecture Notes
Basic Topology of 3-Manifolds
Textbook in Problems on Elementary Topology
Introduction to Topology of Real Algebraic Varieties
Foliations and the topology of 3-manifolds
Topology Without Tears
Ends of complexes
General Topology and Real Analysis
Introduction to Topological Groups
Topology Lecture Notes
Manifold Theory
Topology of Stratified Spaces
Natural Topology
General Topology
Notes on Introductory Point-Set Topology
Topologie des espaces metriques
Metric and Topological Spaces

Home |  Authors | About | Contact Us |  Email 
 Copyright © 2002-2013 FreeScience.info. 

Best viewed with Mozilla 1.X 1024x768
free scientific books