## Illinois Journal of Mathematics

- Illinois J. Math.
- Volume 25, Issue 1 (1981), 136-146.

### Order of the canonical vector bundle on $C_{n}(K)/\Sigma_{k}$

#### Abstract

It has been proved that the order of the naturally defined vector bundle on $C_{n}(K)/\Sigma_{k}$, the configuration space of $k$ distinct points in $R^{n}$, is helpful in finding some new elements of maps between spheres. Now, with the help of representation ring, we give some partial results concerning the largest powers of prime numbers dividing the orders.

#### Article information

**Source**

Illinois J. Math., Volume 25, Issue 1 (1981), 136-146.

**Dates**

First available in Project Euclid: 20 October 2009

**Permanent link to this document**

https://projecteuclid.org/euclid.ijm/1256047373

**Digital Object Identifier**

doi:10.1215/ijm/1256047373

**Mathematical Reviews number (MathSciNet)**

MR602904

**Zentralblatt MATH identifier**

0439.55012

**Subjects**

Primary: 55P35: Loop spaces

Secondary: 55N15: $K$-theory [See also 19Lxx] {For algebraic $K$-theory, see 18F25, 19- XX}

#### Citation

Yang, Su-Win. Order of the canonical vector bundle on $C_{n}(K)/\Sigma_{k}$. Illinois J. Math. 25 (1981), no. 1, 136--146. doi:10.1215/ijm/1256047373. https://projecteuclid.org/euclid.ijm/1256047373