Involutions on<i>S</i><sup>6</sup>with 3–dimensional fixed point set

Olbermann, Martin

doi:10.2140/agt.2010.10.1905

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Exotic Conjugation Spaces1

From This We Deduce1

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Cited by 3 publications

(2 citation statements)

References 29 publications

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“…Our last example includes the 3-dimensional conjugation spheres Olbermann studies very thoroughly in [19]. He shows that every F-homology 3-sphere is the fixed point set of an involution on S 6 .…”

Section: Exotic Conjugation Spacesmentioning

confidence: 99%

Realizing doubles: a conjugation zoo

Pitsch

Scherer

2020

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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Conjugation spaces are topological spaces equipped with an involution such that their fixed points have the same mod 2 cohomology (as a graded vector space, a ring, and even an unstable algebra) but with all degrees divided by two, generalizing the classical examples of complex projective spaces under complex conjugation. Spaces which are constructed from unit balls in complex Euclidean spaces are called spherical and are very well understood. Our aim is twofold. We construct "exotic" conjugation spaces and study the realization question: which spaces can be realized as real loci, i.e., fixed points of conjugation spaces. We identify obstructions and provide examples of spaces and manifolds which cannot be realized as such.

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Section: Exotic Conjugation Spacesmentioning

confidence: 99%

Realizing doubles: a conjugation zoo

Pitsch

Scherer

2020

Proceedings of the Royal Society of Edinburgh: Section A Mathem

View full text Add to dashboard Cite

show abstract

“…In a forthcoming paper [Olb10], we show that our surgery approach to conjugations, and the computation of the transfer map, can be used not only for existence questions, but are also suited to give classification results. In particular we classify all involutions on S 6 with three-dimensional fixed point set.…”

Section: From This We Deducementioning

confidence: 99%