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The geometry and fundamental groups of solenoid complements
ID
Conner, Gregory R.
(
Author
),
ID
Meilstrup, Mark H.
(
Author
),
ID
Repovš, Dušan
(
Author
)
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Abstract
A solenoid is an inverse limit of circles. When a solenoid is embedded in three space, its complement is an open three manifold. We discuss the geometry and fundamental groups of such manifolds, and show that the complements of different solenoids (arising from different inverse limits) have different fundamental groups. Embeddings of the same solenoid can give different groups; in particular, the nicest embeddings are unknotted at each level, and give an Abelian fundamental group, while other embeddings have non-Abelian groups. We show using geometry that every solenoid has uncountably many embeddings with nonhomeomorphic complements.
Language:
English
Keywords:
solenoid
,
3-manifold
,
inverse limit
,
embedding
,
fundamental group
,
knot complement
,
braid
,
Jaco-Shalen-Johannson decomposition
,
Mostow-Prasad rigidity
Work type:
Article
Typology:
1.01 - Original Scientific Article
Organization:
PEF - Faculty of Education
FMF - Faculty of Mathematics and Physics
Year:
2015
Number of pages:
20 str.
Numbering:
Vol. 24, iss. 14
PID:
20.500.12556/RUL-111223
UDC:
515.162
ISSN on article:
0218-2165
DOI:
10.1142/S0218216515500698
COBISS.SI-ID:
17540697
Publication date in RUL:
26.09.2019
Views:
986
Downloads:
515
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Record is a part of a journal
Title:
Journal of knot theory and its ramifications
Shortened title:
J. knot theory ramif.
Publisher:
World Scientific
ISSN:
0218-2165
COBISS.SI-ID:
3996249
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