Twisted conjugacy in PL-homeomorphism groups of the circle
Given an automorphism ϕ : Γ → Γ of a group, one has a left action of Γ on itself defined as g . x = g x ϕ ( g - 1 ) . The orbits of this action are called the Reidemeister classes or ϕ -twisted conjugacy classes. We denote by R ( ϕ ) ∈ N ∪ { ∞ } the Reidemeister number of ϕ , namely, the cardinality...
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| Veröffentlicht in: | Geometriae dedicata 2019-10, Vol.202 (1), p.311-320 |
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| creator | Gonçalves, Daciberg Lima Sankaran, Parameswaran |
| description | Given an automorphism
ϕ
:
Γ
→
Γ
of a group, one has a left action of
Γ
on itself defined as
g
.
x
=
g
x
ϕ
(
g
-
1
)
. The orbits of this action are called the Reidemeister classes or
ϕ
-twisted conjugacy classes. We denote by
R
(
ϕ
)
∈
N
∪
{
∞
}
the Reidemeister number of
ϕ
, namely, the cardinality of the orbit space
R
(
ϕ
)
if it is finite and
R
(
ϕ
)
=
∞
if
R
(
ϕ
)
is infinite. The group
Γ
is said to have the
R
∞
-property if
R
(
ϕ
)
=
∞
for all automorphisms
ϕ
∈
Aut
(
Γ
)
. We show that the generalized Thompson group
T
(
r
,
A
,
P
) has the
R
∞
-property when the slope group
P
⊂
R
>
0
×
is not cyclic. |
| doi_str_mv | 10.1007/s10711-018-0414-6 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2287519765</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2287519765</sourcerecordid><originalsourceid>FETCH-LOGICAL-c316t-45034247a38def7ecfbc9b544748a6aa5a1ec03ca6b33fd1313a321639d63d663</originalsourceid><addsrcrecordid>eNp1kM1Kw0AURgdRsFYfwN2A69F7M3-JOylahYIu6nqYTiZtSpOJMwnStzclgitXd3O-c-EQcotwjwD6ISFoRAaYMxAomDojM5Q6YwWq_JzMAIRiUkt5Sa5S2gNAoXU2I4_r7zr1vqQutPtha92R1i39WLFdaHxoQux2dWroNoahSzRUtN956uroDv6aXFT2kPzN752Tz5fn9eKVrd6Xb4unFXMcVc-EBC4yoS3PS19p76qNKzZSCC1yq6yVFr0D7qzacF6VyJFbnqHiRal4qRSfk7vJ28XwNfjUm30YYju-NFmWa4mFVnKkcKJcDClFX5ku1o2NR4NgTonMlMiMicwpkTmZs2mTRrbd-vhn_n_0A6v4Z_0</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2287519765</pqid></control><display><type>article</type><title>Twisted conjugacy in PL-homeomorphism groups of the circle</title><source>Springer Nature - Complete Springer Journals</source><creator>Gonçalves, Daciberg Lima ; Sankaran, Parameswaran</creator><creatorcontrib>Gonçalves, Daciberg Lima ; Sankaran, Parameswaran</creatorcontrib><description>Given an automorphism
ϕ
:
Γ
→
Γ
of a group, one has a left action of
Γ
on itself defined as
g
.
x
=
g
x
ϕ
(
g
-
1
)
. The orbits of this action are called the Reidemeister classes or
ϕ
-twisted conjugacy classes. We denote by
R
(
ϕ
)
∈
N
∪
{
∞
}
the Reidemeister number of
ϕ
, namely, the cardinality of the orbit space
R
(
ϕ
)
if it is finite and
R
(
ϕ
)
=
∞
if
R
(
ϕ
)
is infinite. The group
Γ
is said to have the
R
∞
-property if
R
(
ϕ
)
=
∞
for all automorphisms
ϕ
∈
Aut
(
Γ
)
. We show that the generalized Thompson group
T
(
r
,
A
,
P
) has the
R
∞
-property when the slope group
P
⊂
R
>
0
×
is not cyclic.</description><identifier>ISSN: 0046-5755</identifier><identifier>EISSN: 1572-9168</identifier><identifier>DOI: 10.1007/s10711-018-0414-6</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Algebraic Geometry ; Automorphisms ; Convex and Discrete Geometry ; Differential Geometry ; Hyperbolic Geometry ; Mathematics ; Mathematics and Statistics ; Original Paper ; Projective Geometry ; Topology</subject><ispartof>Geometriae dedicata, 2019-10, Vol.202 (1), p.311-320</ispartof><rights>Springer Nature B.V. 2018</rights><rights>Copyright Springer Nature B.V. 2019</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-45034247a38def7ecfbc9b544748a6aa5a1ec03ca6b33fd1313a321639d63d663</citedby><cites>FETCH-LOGICAL-c316t-45034247a38def7ecfbc9b544748a6aa5a1ec03ca6b33fd1313a321639d63d663</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10711-018-0414-6$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10711-018-0414-6$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51298</link.rule.ids></links><search><creatorcontrib>Gonçalves, Daciberg Lima</creatorcontrib><creatorcontrib>Sankaran, Parameswaran</creatorcontrib><title>Twisted conjugacy in PL-homeomorphism groups of the circle</title><title>Geometriae dedicata</title><addtitle>Geom Dedicata</addtitle><description>Given an automorphism
ϕ
:
Γ
→
Γ
of a group, one has a left action of
Γ
on itself defined as
g
.
x
=
g
x
ϕ
(
g
-
1
)
. The orbits of this action are called the Reidemeister classes or
ϕ
-twisted conjugacy classes. We denote by
R
(
ϕ
)
∈
N
∪
{
∞
}
the Reidemeister number of
ϕ
, namely, the cardinality of the orbit space
R
(
ϕ
)
if it is finite and
R
(
ϕ
)
=
∞
if
R
(
ϕ
)
is infinite. The group
Γ
is said to have the
R
∞
-property if
R
(
ϕ
)
=
∞
for all automorphisms
ϕ
∈
Aut
(
Γ
)
. We show that the generalized Thompson group
T
(
r
,
A
,
P
) has the
R
∞
-property when the slope group
P
⊂
R
>
0
×
is not cyclic.</description><subject>Algebraic Geometry</subject><subject>Automorphisms</subject><subject>Convex and Discrete Geometry</subject><subject>Differential Geometry</subject><subject>Hyperbolic Geometry</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Original Paper</subject><subject>Projective Geometry</subject><subject>Topology</subject><issn>0046-5755</issn><issn>1572-9168</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp1kM1Kw0AURgdRsFYfwN2A69F7M3-JOylahYIu6nqYTiZtSpOJMwnStzclgitXd3O-c-EQcotwjwD6ISFoRAaYMxAomDojM5Q6YwWq_JzMAIRiUkt5Sa5S2gNAoXU2I4_r7zr1vqQutPtha92R1i39WLFdaHxoQux2dWroNoahSzRUtN956uroDv6aXFT2kPzN752Tz5fn9eKVrd6Xb4unFXMcVc-EBC4yoS3PS19p76qNKzZSCC1yq6yVFr0D7qzacF6VyJFbnqHiRal4qRSfk7vJ28XwNfjUm30YYju-NFmWa4mFVnKkcKJcDClFX5ku1o2NR4NgTonMlMiMicwpkTmZs2mTRrbd-vhn_n_0A6v4Z_0</recordid><startdate>20191001</startdate><enddate>20191001</enddate><creator>Gonçalves, Daciberg Lima</creator><creator>Sankaran, Parameswaran</creator><general>Springer Netherlands</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20191001</creationdate><title>Twisted conjugacy in PL-homeomorphism groups of the circle</title><author>Gonçalves, Daciberg Lima ; Sankaran, Parameswaran</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-45034247a38def7ecfbc9b544748a6aa5a1ec03ca6b33fd1313a321639d63d663</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Algebraic Geometry</topic><topic>Automorphisms</topic><topic>Convex and Discrete Geometry</topic><topic>Differential Geometry</topic><topic>Hyperbolic Geometry</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Original Paper</topic><topic>Projective Geometry</topic><topic>Topology</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Gonçalves, Daciberg Lima</creatorcontrib><creatorcontrib>Sankaran, Parameswaran</creatorcontrib><collection>CrossRef</collection><jtitle>Geometriae dedicata</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gonçalves, Daciberg Lima</au><au>Sankaran, Parameswaran</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Twisted conjugacy in PL-homeomorphism groups of the circle</atitle><jtitle>Geometriae dedicata</jtitle><stitle>Geom Dedicata</stitle><date>2019-10-01</date><risdate>2019</risdate><volume>202</volume><issue>1</issue><spage>311</spage><epage>320</epage><pages>311-320</pages><issn>0046-5755</issn><eissn>1572-9168</eissn><abstract>Given an automorphism
ϕ
:
Γ
→
Γ
of a group, one has a left action of
Γ
on itself defined as
g
.
x
=
g
x
ϕ
(
g
-
1
)
. The orbits of this action are called the Reidemeister classes or
ϕ
-twisted conjugacy classes. We denote by
R
(
ϕ
)
∈
N
∪
{
∞
}
the Reidemeister number of
ϕ
, namely, the cardinality of the orbit space
R
(
ϕ
)
if it is finite and
R
(
ϕ
)
=
∞
if
R
(
ϕ
)
is infinite. The group
Γ
is said to have the
R
∞
-property if
R
(
ϕ
)
=
∞
for all automorphisms
ϕ
∈
Aut
(
Γ
)
. We show that the generalized Thompson group
T
(
r
,
A
,
P
) has the
R
∞
-property when the slope group
P
⊂
R
>
0
×
is not cyclic.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s10711-018-0414-6</doi><tpages>10</tpages></addata></record> |
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| ispartof | Geometriae dedicata, 2019-10, Vol.202 (1), p.311-320 |
| issn | 0046-5755 1572-9168 |
| language | eng |
| recordid | cdi_proquest_journals_2287519765 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Algebraic Geometry Automorphisms Convex and Discrete Geometry Differential Geometry Hyperbolic Geometry Mathematics Mathematics and Statistics Original Paper Projective Geometry Topology |
| title | Twisted conjugacy in PL-homeomorphism groups of the circle |
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