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The Brouwer Fixed Point Theorem for Some Set Mappings

Dariusz Miklaszewski (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

For some classes X 2 of closed subsets of the disc ₙ ⊂ ℝⁿ we prove that every Hausdorff-continuous mapping f: X → X has a fixed point A ∈ X in the sense that the intersection A ∩ f(A) is nonempty.

The center of a graded connected Lie algebra is a nice ideal

Yves Félix (1996)

Annales de l'institut Fourier

Let ( 𝕃 ( V ) , d ) be a free graded connected differential Lie algebra over the field of rational numbers. An ideal I in the Lie algebra H ( 𝕃 ( V ) , d ) is called nice if, for every cycle α 𝕃 ( V ) such that [ α ] belongs to I , the kernel of the map H ( 𝕃 ( V ) , d ) H ( 𝕃 ( V x ) , d ) , d ( x ) = α , is contained in I . We show that the center of H ( 𝕃 ( V ) , d ) is a nice ideal and we give in that case some informations on the structure of the Lie algebra H ( 𝕃 ( V x ) , d ) . We apply this computation for the determination of the rational homotopy Lie algebra L X = π * ( Ω X ) of a simply connected space X . We deduce that the...

The classification of weighted projective spaces

Anthony Bahri, Matthias Franz, Dietrich Notbohm, Nigel Ray (2013)

Fundamenta Mathematicae

We obtain two classifications of weighted projective spaces: up to hoeomorphism and up to homotopy equivalence. We show that the former coincides with Al Amrani's classification up to isomorphism of algebraic varieties, and deduce the latter by proving that the Mislin genus of any weighted projective space is rigid.

The cobordism of Real manifolds

Po Hu (1999)

Fundamenta Mathematicae

We calculate completely the Real cobordism groups, introduced by Landweber and Fujii, in terms of homotopy groups of known spectra.

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