On the homotopy fixed point sets of circle actions on product spaces
For arbitrary S 1 -actions on S Q m , S Q n , and S Q m × S Q n , we show the conditions for the tenability of the homotopy equivalence ( S Q m ) h S 1 × ( S Q n ) h S 1 ≃ ( S Q m × S Q n ) h S 1 . Here, X h S 1 denotes the homotopy fixed point set of an S 1 -action on an space X .
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| Veröffentlicht in: | Archiv der Mathematik 2021, Vol.116 (1), p.97-105 |
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| container_title | Archiv der Mathematik |
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| creator | Liu, Jian Xie, Sang Liu, Xiugui |
| description | For arbitrary
S
1
-actions on
S
Q
m
,
S
Q
n
, and
S
Q
m
×
S
Q
n
, we show the conditions for the tenability of the homotopy equivalence
(
S
Q
m
)
h
S
1
×
(
S
Q
n
)
h
S
1
≃
(
S
Q
m
×
S
Q
n
)
h
S
1
. Here,
X
h
S
1
denotes the homotopy fixed point set of an
S
1
-action on an space
X
. |
| doi_str_mv | 10.1007/s00013-020-01512-w |
| format | Article |
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S
1
-actions on
S
Q
m
,
S
Q
n
, and
S
Q
m
×
S
Q
n
, we show the conditions for the tenability of the homotopy equivalence
(
S
Q
m
)
h
S
1
×
(
S
Q
n
)
h
S
1
≃
(
S
Q
m
×
S
Q
n
)
h
S
1
. Here,
X
h
S
1
denotes the homotopy fixed point set of an
S
1
-action on an space
X
.</description><identifier>ISSN: 0003-889X</identifier><identifier>EISSN: 1420-8938</identifier><identifier>DOI: 10.1007/s00013-020-01512-w</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Mathematics ; Mathematics and Statistics</subject><ispartof>Archiv der Mathematik, 2021, Vol.116 (1), p.97-105</ispartof><rights>Springer Nature Switzerland AG 2020</rights><rights>Springer Nature Switzerland AG 2020.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-e8a3960d803927f7f63eb467d25153706cd3b5c0ee0ebdb42e6e99c79b5485693</cites><orcidid>0000-0002-8787-3116</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00013-020-01512-w$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00013-020-01512-w$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,778,782,27911,27912,41475,42544,51306</link.rule.ids></links><search><creatorcontrib>Liu, Jian</creatorcontrib><creatorcontrib>Xie, Sang</creatorcontrib><creatorcontrib>Liu, Xiugui</creatorcontrib><title>On the homotopy fixed point sets of circle actions on product spaces</title><title>Archiv der Mathematik</title><addtitle>Arch. Math</addtitle><description>For arbitrary
S
1
-actions on
S
Q
m
,
S
Q
n
, and
S
Q
m
×
S
Q
n
, we show the conditions for the tenability of the homotopy equivalence
(
S
Q
m
)
h
S
1
×
(
S
Q
n
)
h
S
1
≃
(
S
Q
m
×
S
Q
n
)
h
S
1
. Here,
X
h
S
1
denotes the homotopy fixed point set of an
S
1
-action on an space
X
.</description><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>0003-889X</issn><issn>1420-8938</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kEFLAzEQhYMoWKt_wFPA8-ok2d0kR6lahUIvCt7CbnbWbmk3a5JS--9NXcGbp2FmvvcePEKuGdwyAHkXAICJDDhkwArGs_0JmbA8rUoLdUom6S8ypfT7ObkIYZ1orqSekIdlT-MK6cptXXTDgbbdFzZ0cF0facAYqGup7bzdIK1s7FyfLj0dvGt2NhFDZTFckrO22gS8-p1T8vb0-Dp7zhbL-cvsfpFZLiFmqCqhS2gUCM1lK9tSYJ2XsuEFK4SE0jaiLiwgAtZNnXMsUWsrdV3kqii1mJKb0TfFf-4wRLN2O9-nSMNzqY--qkwUHynrXQgeWzP4blv5g2Fgjm2ZsS2T2jI_bZl9EolRFBLcf6D_s_5H9Q3xtWzB</recordid><startdate>2021</startdate><enddate>2021</enddate><creator>Liu, Jian</creator><creator>Xie, Sang</creator><creator>Liu, Xiugui</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-8787-3116</orcidid></search><sort><creationdate>2021</creationdate><title>On the homotopy fixed point sets of circle actions on product spaces</title><author>Liu, Jian ; Xie, Sang ; Liu, Xiugui</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-e8a3960d803927f7f63eb467d25153706cd3b5c0ee0ebdb42e6e99c79b5485693</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Liu, Jian</creatorcontrib><creatorcontrib>Xie, Sang</creatorcontrib><creatorcontrib>Liu, Xiugui</creatorcontrib><collection>CrossRef</collection><jtitle>Archiv der Mathematik</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Liu, Jian</au><au>Xie, Sang</au><au>Liu, Xiugui</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the homotopy fixed point sets of circle actions on product spaces</atitle><jtitle>Archiv der Mathematik</jtitle><stitle>Arch. Math</stitle><date>2021</date><risdate>2021</risdate><volume>116</volume><issue>1</issue><spage>97</spage><epage>105</epage><pages>97-105</pages><issn>0003-889X</issn><eissn>1420-8938</eissn><abstract>For arbitrary
S
1
-actions on
S
Q
m
,
S
Q
n
, and
S
Q
m
×
S
Q
n
, we show the conditions for the tenability of the homotopy equivalence
(
S
Q
m
)
h
S
1
×
(
S
Q
n
)
h
S
1
≃
(
S
Q
m
×
S
Q
n
)
h
S
1
. Here,
X
h
S
1
denotes the homotopy fixed point set of an
S
1
-action on an space
X
.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00013-020-01512-w</doi><tpages>9</tpages><orcidid>https://orcid.org/0000-0002-8787-3116</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0003-889X |
| ispartof | Archiv der Mathematik, 2021, Vol.116 (1), p.97-105 |
| issn | 0003-889X 1420-8938 |
| language | eng |
| recordid | cdi_proquest_journals_2479803986 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Mathematics Mathematics and Statistics |
| title | On the homotopy fixed point sets of circle actions on product spaces |
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