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arXiv · 2607.00298

The real $K$-theory of the sphere with an arbitrary involution

Jeffrey L. Boersema
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Abstract

We complete the investigation begun in a previous paper to find unitary representations of the non-trivial real $K$-theory elements for the sphere $S^d$ with an involution. Here we consider all involutions except the antipodal involutions. We write down explicit unitaries representing the generators in all cases for $d \leq 3$, and for $d > 0$ we describe a recipe for generating such unitaries.

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Jeffrey L. Boersema. 2026-07-01. The real $K$-theory of the sphere with an arbitrary involution. https://arxiv.org/abs/2607.00298

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