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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 n , n ≥ 2, π n ( n , o ) ω and π i ( 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 types of one-dimensional Peano continua

Katsuya Eda (2010)

Fundamenta Mathematicae

Let X and Y be one-dimensional Peano continua. If the fundamental groups of X and Y are isomorphic, then X and Y are homotopy equivalent. Every homomorphism from the fundamental group of X to that of Y is a composition of a homomorphism induced from a continuous map and a base point change isomorphism.

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