On flat manifold bundles and the connectivity of Haefliger’s classifying spaces
We investigate a conjecture due to Haefliger and Thurston in the context of foliated manifold bundles. In this context, Haefliger-Thurston’s conjecture predicts that every M M -bundle over a manifold B B where dim ( B ) ≤ dim ( M ) \operatorname {dim}(B)\leq \operatorname {dim}(M) is cobordant t...
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| Veröffentlicht in: | Proceedings of the American Mathematical Society 2024-11, Vol.152 (11), p.4943-4957 |
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| container_title | Proceedings of the American Mathematical Society |
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| creator | Nariman, Sam |
| description | We investigate a conjecture due to Haefliger and Thurston in the context of foliated manifold bundles. In this context, Haefliger-Thurston’s conjecture predicts that every
M
M
-bundle over a manifold
B
B
where
dim
(
B
)
≤
dim
(
M
)
\operatorname {dim}(B)\leq \operatorname {dim}(M)
is cobordant to a flat
M
M
-bundle. In particular, we study the bordism class of flat
M
M
-bundles over low dimensional manifolds, comparing a finite dimensional Lie group
G
G
with
D
i
f
f
0
(
G
)
\mathrm {Diff}_0(G)
. |
| doi_str_mv | 10.1090/proc/16941 |
| format | Article |
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M
M
-bundle over a manifold
B
B
where
dim
(
B
)
≤
dim
(
M
)
\operatorname {dim}(B)\leq \operatorname {dim}(M)
is cobordant to a flat
M
M
-bundle. In particular, we study the bordism class of flat
M
M
-bundles over low dimensional manifolds, comparing a finite dimensional Lie group
G
G
with
D
i
f
f
0
(
G
)
\mathrm {Diff}_0(G)
.</description><identifier>ISSN: 0002-9939</identifier><identifier>EISSN: 1088-6826</identifier><identifier>DOI: 10.1090/proc/16941</identifier><language>eng</language><ispartof>Proceedings of the American Mathematical Society, 2024-11, Vol.152 (11), p.4943-4957</ispartof><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c120t-3e0dd7c7e2441dd03ce1d4187987929a091abac9c2050b685607b724e55a9d683</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27903,27904</link.rule.ids></links><search><creatorcontrib>Nariman, Sam</creatorcontrib><title>On flat manifold bundles and the connectivity of Haefliger’s classifying spaces</title><title>Proceedings of the American Mathematical Society</title><description>We investigate a conjecture due to Haefliger and Thurston in the context of foliated manifold bundles. In this context, Haefliger-Thurston’s conjecture predicts that every
M
M
-bundle over a manifold
B
B
where
dim
(
B
)
≤
dim
(
M
)
\operatorname {dim}(B)\leq \operatorname {dim}(M)
is cobordant to a flat
M
M
-bundle. In particular, we study the bordism class of flat
M
M
-bundles over low dimensional manifolds, comparing a finite dimensional Lie group
G
G
with
D
i
f
f
0
(
G
)
\mathrm {Diff}_0(G)
.</description><issn>0002-9939</issn><issn>1088-6826</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNot0MtKAzEYBeAgCo7VjU-QtTD2TyaTy1KKWqFQBF0PmVxqJM2UZBRm52v4ej5JWxUOHM7mLD6ErgncElAw3-XBzAlXjJygioCUNZeUn6IKAGitVKPO0UUp74dJFBMVel4n7KMe8Van4Idocf-RbHQF62Tx-OawGVJyZgyfYZzw4PFSOx_DxuWfr--CTdSlBD-FtMFlp40rl-jM61jc1X_P0OvD_ctiWa_Wj0-Lu1VtCIWxbhxYK4xwlDFiLTTGEcuIFOoQqjQoonttlKHQQs9ly0H0gjLXtlpZLpsZuvn7NXkoJTvf7XLY6jx1BLojRnfE6H4xmj1DvVP1</recordid><startdate>202411</startdate><enddate>202411</enddate><creator>Nariman, Sam</creator><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>202411</creationdate><title>On flat manifold bundles and the connectivity of Haefliger’s classifying spaces</title><author>Nariman, Sam</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c120t-3e0dd7c7e2441dd03ce1d4187987929a091abac9c2050b685607b724e55a9d683</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Nariman, Sam</creatorcontrib><collection>CrossRef</collection><jtitle>Proceedings of the American Mathematical Society</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Nariman, Sam</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On flat manifold bundles and the connectivity of Haefliger’s classifying spaces</atitle><jtitle>Proceedings of the American Mathematical Society</jtitle><date>2024-11</date><risdate>2024</risdate><volume>152</volume><issue>11</issue><spage>4943</spage><epage>4957</epage><pages>4943-4957</pages><issn>0002-9939</issn><eissn>1088-6826</eissn><abstract>We investigate a conjecture due to Haefliger and Thurston in the context of foliated manifold bundles. In this context, Haefliger-Thurston’s conjecture predicts that every
M
M
-bundle over a manifold
B
B
where
dim
(
B
)
≤
dim
(
M
)
\operatorname {dim}(B)\leq \operatorname {dim}(M)
is cobordant to a flat
M
M
-bundle. In particular, we study the bordism class of flat
M
M
-bundles over low dimensional manifolds, comparing a finite dimensional Lie group
G
G
with
D
i
f
f
0
(
G
)
\mathrm {Diff}_0(G)
.</abstract><doi>10.1090/proc/16941</doi><tpages>15</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0002-9939 |
| ispartof | Proceedings of the American Mathematical Society, 2024-11, Vol.152 (11), p.4943-4957 |
| issn | 0002-9939 1088-6826 |
| language | eng |
| recordid | cdi_crossref_primary_10_1090_proc_16941 |
| source | American Mathematical Society Publications |
| title | On flat manifold bundles and the connectivity of Haefliger’s classifying spaces |
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