On modular cohomotopy groups
Let p be a prime and let π n ( X ; ℤ/ p r ) = [ X, M n (ℤ/ p r )] be the set of homotopy classes of based maps from CW-complexes X into the mod p r Moore spaces M n (ℤ/ p r ) of degree n , where ℤ/ p r denotes the integers mod p r . In this paper we firstly determine the modular cohomotopy groups π...
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| Veröffentlicht in: | Israel journal of mathematics 2023-03, Vol.253 (2), p.887-915 |
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| container_title | Israel journal of mathematics |
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| creator | Li, Pengcheng Pan, Jianzhong Wu, Jie |
| description | Let
p
be a prime and let
π
n
(
X
; ℤ/
p
r
) = [
X, M
n
(ℤ/
p
r
)] be the set of homotopy classes of based maps from CW-complexes
X
into the mod
p
r
Moore spaces
M
n
(ℤ/
p
r
) of degree
n
, where ℤ/
p
r
denotes the integers mod
p
r
. In this paper we firstly determine the modular cohomotopy groups
π
n
(
X
; ℤ/
p
r
) up to extensions by classical methods of primary cohomology operations and give conditions for the splitness of the extensions. Secondly we utilize some unstable homotopy theory of Moore spaces to study the modular cohomotopy groups; especially, the group
π
3
(
X
; ℤ
(2)
) with dim(
X
) ≤ 6 is determined. |
| doi_str_mv | 10.1007/s11856-022-2409-0 |
| format | Article |
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p
be a prime and let
π
n
(
X
; ℤ/
p
r
) = [
X, M
n
(ℤ/
p
r
)] be the set of homotopy classes of based maps from CW-complexes
X
into the mod
p
r
Moore spaces
M
n
(ℤ/
p
r
) of degree
n
, where ℤ/
p
r
denotes the integers mod
p
r
. In this paper we firstly determine the modular cohomotopy groups
π
n
(
X
; ℤ/
p
r
) up to extensions by classical methods of primary cohomology operations and give conditions for the splitness of the extensions. Secondly we utilize some unstable homotopy theory of Moore spaces to study the modular cohomotopy groups; especially, the group
π
3
(
X
; ℤ
(2)
) with dim(
X
) ≤ 6 is determined.</description><identifier>ISSN: 0021-2172</identifier><identifier>EISSN: 1565-8511</identifier><identifier>DOI: 10.1007/s11856-022-2409-0</identifier><language>eng</language><publisher>Jerusalem: The Hebrew University Magnes Press</publisher><subject>Algebra ; Analysis ; Applications of Mathematics ; Group Theory and Generalizations ; Homology ; Homotopy theory ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Theoretical</subject><ispartof>Israel journal of mathematics, 2023-03, Vol.253 (2), p.887-915</ispartof><rights>The Hebrew University of Jerusalem 2022</rights><rights>The Hebrew University of Jerusalem 2022.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c268t-b2e057e94eb90cf5fb07d264cd0c039bfbb05f6f029653593bc564c3fd1e661e3</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/s11856-022-2409-0$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11856-022-2409-0$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Li, Pengcheng</creatorcontrib><creatorcontrib>Pan, Jianzhong</creatorcontrib><creatorcontrib>Wu, Jie</creatorcontrib><title>On modular cohomotopy groups</title><title>Israel journal of mathematics</title><addtitle>Isr. J. Math</addtitle><description>Let
p
be a prime and let
π
n
(
X
; ℤ/
p
r
) = [
X, M
n
(ℤ/
p
r
)] be the set of homotopy classes of based maps from CW-complexes
X
into the mod
p
r
Moore spaces
M
n
(ℤ/
p
r
) of degree
n
, where ℤ/
p
r
denotes the integers mod
p
r
. In this paper we firstly determine the modular cohomotopy groups
π
n
(
X
; ℤ/
p
r
) up to extensions by classical methods of primary cohomology operations and give conditions for the splitness of the extensions. Secondly we utilize some unstable homotopy theory of Moore spaces to study the modular cohomotopy groups; especially, the group
π
3
(
X
; ℤ
(2)
) with dim(
X
) ≤ 6 is determined.</description><subject>Algebra</subject><subject>Analysis</subject><subject>Applications of Mathematics</subject><subject>Group Theory and Generalizations</subject><subject>Homology</subject><subject>Homotopy theory</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Theoretical</subject><issn>0021-2172</issn><issn>1565-8511</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp1kEFLxDAQhYMoWFd_gOCh4Dk6M2nS9iiLrsLCXvQcmjRZXbZNTbaH_fd2qeDJ0xze-97Ax9gtwgMClI8JsZKKAxGnAmoOZyxDqSSvJOI5ywAIOWFJl-wqpR2AFCWKjN1t-rwL7bhvYm7DZ-jCIQzHfBvDOKRrduGbfXI3v3fBPl6e35evfL1ZvS2f1tySqg7ckANZurpwpgbrpTdQtqQK24IFURtvDEivPFCtpJC1MFZOqfAtOqXQiQW7n3eHGL5Hlw56F8bYTy81VYBUVkIUUwvnlo0hpei8HuJX18SjRtAnCXqWoCcJ-iRBw8TQzKSp229d_Fv-H_oB-ltdaA</recordid><startdate>20230301</startdate><enddate>20230301</enddate><creator>Li, Pengcheng</creator><creator>Pan, Jianzhong</creator><creator>Wu, Jie</creator><general>The Hebrew University Magnes Press</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20230301</creationdate><title>On modular cohomotopy groups</title><author>Li, Pengcheng ; Pan, Jianzhong ; Wu, Jie</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c268t-b2e057e94eb90cf5fb07d264cd0c039bfbb05f6f029653593bc564c3fd1e661e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Algebra</topic><topic>Analysis</topic><topic>Applications of Mathematics</topic><topic>Group Theory and Generalizations</topic><topic>Homology</topic><topic>Homotopy theory</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Li, Pengcheng</creatorcontrib><creatorcontrib>Pan, Jianzhong</creatorcontrib><creatorcontrib>Wu, Jie</creatorcontrib><collection>CrossRef</collection><jtitle>Israel journal of mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Li, Pengcheng</au><au>Pan, Jianzhong</au><au>Wu, Jie</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On modular cohomotopy groups</atitle><jtitle>Israel journal of mathematics</jtitle><stitle>Isr. J. Math</stitle><date>2023-03-01</date><risdate>2023</risdate><volume>253</volume><issue>2</issue><spage>887</spage><epage>915</epage><pages>887-915</pages><issn>0021-2172</issn><eissn>1565-8511</eissn><abstract>Let
p
be a prime and let
π
n
(
X
; ℤ/
p
r
) = [
X, M
n
(ℤ/
p
r
)] be the set of homotopy classes of based maps from CW-complexes
X
into the mod
p
r
Moore spaces
M
n
(ℤ/
p
r
) of degree
n
, where ℤ/
p
r
denotes the integers mod
p
r
. In this paper we firstly determine the modular cohomotopy groups
π
n
(
X
; ℤ/
p
r
) up to extensions by classical methods of primary cohomology operations and give conditions for the splitness of the extensions. Secondly we utilize some unstable homotopy theory of Moore spaces to study the modular cohomotopy groups; especially, the group
π
3
(
X
; ℤ
(2)
) with dim(
X
) ≤ 6 is determined.</abstract><cop>Jerusalem</cop><pub>The Hebrew University Magnes Press</pub><doi>10.1007/s11856-022-2409-0</doi><tpages>29</tpages></addata></record> |
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| identifier | ISSN: 0021-2172 |
| ispartof | Israel journal of mathematics, 2023-03, Vol.253 (2), p.887-915 |
| issn | 0021-2172 1565-8511 |
| language | eng |
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| source | SpringerLink Journals - AutoHoldings |
| subjects | Algebra Analysis Applications of Mathematics Group Theory and Generalizations Homology Homotopy theory Mathematical and Computational Physics Mathematics Mathematics and Statistics Theoretical |
| title | On modular cohomotopy groups |
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