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Limiting Cases of Boardman’s Five Halves Theorem
- Part of
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 59 / Issue 2 / May 2016
- Published online by Cambridge University Press:
- 15 March 2016, pp. 359-361
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Limiting cases of Boardman's five halves theorem
- Part of
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 56 / Issue 3 / October 2013
- Published online by Cambridge University Press:
- 28 June 2013, pp. 723-732
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The famous five halves theorem of Boardman states that, if T: Mm → Mm is a smooth involution defined on a non-bounding closed smooth m-dimensional manifold Mm (m > 1) and if
is the fixed-point set of T, where Fj denotes the union of those components of F having dimension j, then 2m ≤ 5n. If the dimension m is written as m = 5k − c, where k ≥ 1 and 0 ≤ c < 5, the theorem states that the dimension n of the fixed submanifold is at least β(m), where β(m) = 2k if c = 0, 1, 2 and β(m) = 2k − 1 if c = 3, 4. In this paper, we give, for each m > 1, the equivariant cobordism classification of involutions (Mm, T), for which the fixed submanifold F attains the minimal dimension β(m).
