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Finite Subgroups of SO(4)

Kimberly Druschel, SLU

What
  • Geometry/ Topology Seminar
  • Topology Seminar
When Tue, Nov 10, 2015
from 02:10 PM to 03:00 PM
Where 346 Ritter Hall
Contact Name
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The finite subgroups of SO(3) are the dihedral groups and the three symmetry groups of Platonic solids: the tetrahedron, octahedron, and icosahedron groups, which are in turn the alternating and symmetric groups A4, S4, and A5.

The multiplication of quaternions leads nicely to a determination of the finite subgroups of SO(4), the special orthogonal group of dimension four real matrices. There are many infinite families of such groups, and as for SO(3), some individual groups which relate to symmetries of regular polytopes. We will derive this list and look at some of the groups' properties and specific examples, including symplectic groups and symmetry groups of regular four polytopes and quotients by these groups.

This is a background talk for talks I'll give early next semester on orbifolds. There I'll focus on low dimensional orbifolds, particularly those of dimensions four and five, vertex group homology in those degrees, and orbifold cobordism and invariants.

This talk is meant to be accessible to all graduate students.

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