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Homotopy and homology groups of the n-dimensional Hawaiian earring

Katsuya Eda, Kazuhiro Kawamura (2000)

Fundamenta Mathematicae

For the n-dimensional Hawaiian earring ℍ n , n ≥ 2, π n ( ℍ n , o ) ≃ ℤ ω and π i ( ℍ n , o ) is trivial for each 1 ≤ i ≤ n - 1. Let CX be the cone over a space X and CX ∨ CY be the one-point union with two points of the base spaces X and Y being identified to a point. Then H n ( X ∨ Y ) ≃ H n ( X ) ⊕ H n ( Y ) ⊕ H n ( C X ∨ C Y ) for n ≥ 1.

Homotopy classification of nanophrases with at most four letters

Tomonori Fukunaga (2011)

Fundamenta Mathematicae

We give a homotopy classification of nanophrases with at most four letters. It is an extension of the classification of nanophrases of length 2 with at most four letters, given by the author in a previous paper. As a corollary, we give a stable classification of ordered, pointed, oriented multi-component curves on surfaces with minimal crossing number less than or equal to 2 such that any equivalent curve has no simply closed curves in its components.

Homotopy decompositions of orbit spaces and the Webb conjecture

Jolanta Słomińska (2001)

Fundamenta Mathematicae

Let p be a prime number. We prove that if G is a compact Lie group with a non-trivial p-subgroup, then the orbit space ( B p ( G ) ) / G of the classifying space of the category associated to the G-poset p ( G ) of all non-trivial elementary abelian p-subgroups of G is contractible. This gives, for every G-CW-complex X each of whose isotropy groups contains a non-trivial p-subgroup, a decomposition of X/G as a homotopy colimit of the functor X E ₙ / ( N E ₀ ∩ . . . ∩ N E ₙ ) defined over the poset ( s d p ( G ) ) / G , where sd is the barycentric subdivision. We also...

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