Involutions in the topologists' orthogonal group

2016/12/27 by Dugger, Daniel
#20E45 #Algebraic Topology (math.AT) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1612.08487

Abstract

We classify conjugacy classes of involutions in the isometry groups of nondegenerate, symmetric bilinear forms over the field of two elements. The new component of this work focuses on the case of an orthogonal form on an even dimensional space. In this context we show that the involutions satisfy a remarkable duality, and we investigate several numerical invariants.

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