Authors: Blagojević, Pavle 
Grujić, Vladimir
Živaljević, Rade 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Arrangements of symmetric products of spaces
Journal: Topology and its Applications
Volume: 148
Issue: 1-3
First page: 213
Last page: 232
Issue Date: 28-Feb-2005
Rank: M23
ISSN: 0166-8641
DOI: 10.1016/j.topol.2004.09.001
Abstract: 
We study the combinatorics and topology of general arrangements of sub-spaces of the form D + SP n-d (X) in symmetric products SP n (X) where D ∈ SP d (X). Symmetric products SP m (X) : = X m /S m , also known as the spaces of effective "divisors" of order m, together with their companion spaces of divisors/particles, have been studied from many points of view in numerous papers, see [P. Blagojević et al., in: B. Dragović, B. Sazdović (Eds.) Summer School in Modern Mathematical Physics, 2004, math.AT/0408417; S. Kallel, Trans. Amer. Math. Soc. 350 (1998), 1350] for the references. In this paper we approach them from the point of view of geometric combinatorics. Using the topological technique of diagrams of spaces along the lines of [V. Welker et al., J. Reine Angew. Math. 509 (1999), 117; G.M. Ziegler, R.T. Živaljević, Math. Ann. 295 (1993) 527] we calculate the homology of the union and the complement of these arrangements. As an application we include a computation of the homology of the homotopy end space of the open manifold SP n (M g,k ), where M g,k is a Riemann surface of genus g punctured at k points, a problem which was originally motivated by the study of commutative (m + k, m)-groups [K. Trenčevski, D. Dimovski, J. Algebra 240 (2001) 338].
Keywords: Diagrams of spaces | End spaces | Homotopy colimits | Symmetric products
Publisher: Elsevier
Project: Serbian Ministry of Science, Technology and Development, Grant no. 1643
Geometry and Topology of Manifolds and Integrable Dynamical Systems 

Show full item record

SCOPUSTM   
Citations

1
checked on Oct 2, 2022

Page view(s)

21
checked on Sep 15, 2022

Google ScholarTM

Check

Altmetric

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.