scholarly journals The number of homomorphisms from the Hawaiian earring group

2019 ◽  
Vol 523 ◽  
pp. 34-52 ◽  
Author(s):  
Samuel M. Corson
Keyword(s):  
Hawaiian Earring

Embeddings of locally compact abelian p-groups in Hawaiian groups

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Yanga Bavuma ◽  
Francesco G. Russo
Keyword(s):  
Algebraic Topology ◽  
Geometric Interpretation ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Locally Compact Abelian Groups ◽  
Compact Abelian Groups ◽  
Hawaiian Earring ◽  
Path Connected

Abstract We show that locally compact abelian p-groups can be embedded in the first Hawaiian group on a compact path connected subspace of the Euclidean space of dimension four. This result gives a new geometric interpretation for the classification of locally compact abelian groups which are rich in commuting closed subgroups. It is then possible to introduce the idea of an algebraic topology for topologically modular locally compact groups via the geometry of the Hawaiian earring. Among other things, we find applications for locally compact groups which are just noncompact.

The Singular Homology of the Hawaiian Earring

2000 ◽  
Vol 62 (1) ◽  
pp. 305-310 ◽  
Author(s):  
Katsuya Eda ◽  
Kazuhiro Kawamura
Keyword(s):  
Singular Homology ◽  
Hawaiian Earring

On Hawaiian Groups of the Infinite Dimensional Hawaiian Earring

2021 ◽  
pp. 107920
Author(s):  
Ameneh Babaee ◽  
Behrooz Mashayekhy ◽  
Hanieh Mirebrahimi ◽  
Hamid Torabi
Keyword(s):  
Infinite Dimensional ◽  
Hawaiian Earring

scholarly journals A core-free semicovering of the Hawaiian Earring

2013 ◽  
Vol 160 (14) ◽  
pp. 1957-1967 ◽  
Author(s):  
Hanspeter Fischer ◽  
Andreas Zastrow
Keyword(s):  
Hawaiian Earring

scholarly journals Inverse limits of finite rank free groups

2012 ◽  
Vol 15 (6) ◽  
Author(s):  
Gregory R. Conner ◽  
Curtis Kent
Keyword(s):  
Homomorphic Image ◽  
Free Group ◽  
Finite Rank ◽  
Inverse Limit ◽  
Free Groups ◽  
Inverse System ◽  
Inverse Limits ◽  
Universal Group ◽  
Hawaiian Earring ◽  
Constant System

Abstract.We will show that the inverse limit of finite rank free groups with surjective connecting homomorphism is isomorphic either to a finite rank free group or to a fixed universal group. In other words, any inverse system of finite rank free groups which is not equivalent to an eventually constant system has the universal group as its limit. This universal inverse limit is naturally isomorphic to the first shape group of the Hawaiian earring. We also give an example of a homomorphic image of the Hawaiian earring group which lies in the inverse limit of free groups but is neither a free group nor isomorphic to the Hawaiian earring group.

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