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The Euler characteristic of the symmetric product of a finite CW-complex

Kostadin Trenčevski ; Institute of Mathematics, Ss. Cyril and Methodius University, Skopje, Macedonia

Sažetak

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.

Ključne riječi

symmetric products of manifolds; homology; Euler characteristic; orientability

Hrčak ID:

61756

URI

https://hrcak.srce.hr/61756

Datum izdavanja:

8.12.2010.

Posjeta: 2.182 *