Original scientific paper
The Euler characteristic of the symmetric product of a finite CW-complex
Kostadin Trenčevski
; Institute of Mathematics, Ss. Cyril and Methodius University, Skopje, Macedonia
Abstract
In this paper it is first shown that if M is a 2-dimensional
surface, then $M^{(m)}$ is orientable if and only if M is orientable.
Using the Macdonald's result [5].
the Betti numbers of $M^{(m)}$ are expressed explicitely,
the Euler characteristic is found and it depends only on $m$
and the Euler characteristic of M.
Moreover, the formula for the Euler characteristic is proved alternatively also without using the Macdonalds's results.
Keywords
symmetric products of manifolds; homology; Euler characteristic; orientability
Hrčak ID:
61756
URI
Publication date:
8.12.2010.
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