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arXiv · 2506.16612

The $K$-Theory of the Sphere with the Antipodal Involution

Jeffrey L Boersema
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Abstract

This is a thorough investigation on the real $K$-theory of the sphere $S^d$ associated with the antipodal involution. We calculate the algebraic structure of real $K$-theory and united $K$-theory for all $d$, we write down explicit unitaries representing the generators of all the non-trivial $K$-theory groups for $d \leq 4$, and we describe a recipe for generating such unitaries for all $d$.

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Jeffrey L Boersema. 2025-06-19. The $K$-Theory of the Sphere with the Antipodal Involution. https://arxiv.org/abs/2506.16612

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