|Affiliations:||Mathematical Institute of the Serbian Academy of Sciences and Arts||Title:||Symmetric products of surfaces and the cycle index||Journal:||Israel Journal of Mathematics||Volume:||138||First page:||61||Last page:||72||Issue Date:||1-Jan-2003||Rank:||M22||ISSN:||0021-2172||DOI:||10.1007/BF02783419||Abstract:||
We study some of the combinatorial structures related to the signature of G-symmetric products of (open) surfaces SPGm(M) = M m/G where G ⊂ Sm. The attention is focused on the question, what information about a surface M can be recovered from a symmetric product SPn(M). The problem is motivated in part by the study of locally Euclidean topological commutative (m + k, m)-groups, . Emphasizing a combinatorial point of view we express the signature Sign(SPGm(M)) in terms of the cycle index Z(G; x̄) of G, a polynomial which originally appeared in Pólya enumeration theory of graphs, trees, chemical structures etc. The computations are used to show that there exist punctured Riemann surfaces Mg,k, Mg,k, such that the manifolds SPm(Mg,k) and SPm(Mg,k) are often not homeomorphic, although they always have the same homotopy type provided 2g + k = 2g + k and k, k ≥ 1.
|Publisher:||Springer Link||Project:||Geometry and Topology of Manifolds and Integrable Dynamical Systems|
Show full item record
checked on Mar 25, 2023
checked on Mar 26, 2023
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.