## Illinois Journal of Mathematics

### Spin(4) actions on $8$-dimensional manifolds (I)

Philippe Mazaud

#### Abstract

We study smooth Spin(4) actions on closed, orientable $8$-dimensional manifolds, where Spin(4) is isomorphic to the group $\mathrm{SU}(2) \times \mathrm{SU}(2)$. We examine the isotropy structures that can arise, and give an equivariant classification in the case where the set of exceptional orbits, stabilized by finite-cyclic goups, is empty.

#### Article information

Source
Illinois J. Math., Volume 44, Issue 1 (2000), 183-211.

Dates
First available in Project Euclid: 19 October 2009

https://projecteuclid.org/euclid.ijm/1255984959

Digital Object Identifier
doi:10.1215/ijm/1255984959

Mathematical Reviews number (MathSciNet)
MR1731387

Zentralblatt MATH identifier
0945.57015

Subjects
Primary: 57S15: Compact Lie groups of differentiable transformations

#### Citation

Mazaud, Philippe. Spin(4) actions on $8$-dimensional manifolds (I). Illinois J. Math. 44 (2000), no. 1, 183--211. doi:10.1215/ijm/1255984959. https://projecteuclid.org/euclid.ijm/1255984959