Volume-convergent sequences of Haken 3-manifolds
Let M be a closed orientable 3-manifold and let Vol( M) denote its Gromov simplicial volume. This paper is devoted to the study of sequences of non-zero degree maps f i :M→N i to Haken manifolds. We prove that any sequence of Haken manifolds ( N i , f i ), satisfying lim i→∞ deg( f i )×Vol( N i )=Vo...
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| Veröffentlicht in: | Comptes rendus. Mathématique 2003-05, Vol.336 (10), p.833-838 |
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| creator | Derbez, P. |
| description | Let M be a closed orientable 3-manifold and let Vol(
M) denote its Gromov simplicial volume. This paper is devoted to the study of sequences of non-zero degree maps
f
i
:M→N
i
to Haken manifolds. We prove that any sequence of Haken manifolds (
N
i
,
f
i
), satisfying lim
i→∞
deg(
f
i
)×Vol(
N
i
)=Vol(
M) is finite up to homeomorphism. As an application, we deduce from this fact that any closed orientable 3-manifold with zero Gromov simplicial volume and in particular any graph manifold dominates at most finitely many Haken 3-manifolds.
To cite this article: P. Derbez, C. R. Acad. Sci. Paris, Ser. I 336 (2003).
Soit M une 3-variété close orientable et désignons par Vol(
M) le volume simplicial de Gromov de M. Cette Note est consacrée à l'étude des applications de degré non-nul
f
i
:M→N
i
où chaque
N
i
est une variété Haken. Le résultat principal affirme que toute suite (
N
i
,
f
i
) de variétés Haken satisfaisant lim
i→∞
deg(
f
i
)×Vol(
N
i
)=Vol(
M) est finie, à homéomorphisme près. Ce résultat implique en particulier que toute 3-variété close orientable dont le volume simplicial de Gromov est nul (en particulier toute variété graphée) domine au plus un nombre fini de variétés Haken.
Pour citer cet article : P. Derbez, C. R. Acad. Sci. Paris, Ser. I 336 (2003). |
| doi_str_mv | 10.1016/S1631-073X(03)00187-0 |
| format | Article |
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M) denote its Gromov simplicial volume. This paper is devoted to the study of sequences of non-zero degree maps
f
i
:M→N
i
to Haken manifolds. We prove that any sequence of Haken manifolds (
N
i
,
f
i
), satisfying lim
i→∞
deg(
f
i
)×Vol(
N
i
)=Vol(
M) is finite up to homeomorphism. As an application, we deduce from this fact that any closed orientable 3-manifold with zero Gromov simplicial volume and in particular any graph manifold dominates at most finitely many Haken 3-manifolds.
To cite this article: P. Derbez, C. R. Acad. Sci. Paris, Ser. I 336 (2003).
Soit M une 3-variété close orientable et désignons par Vol(
M) le volume simplicial de Gromov de M. Cette Note est consacrée à l'étude des applications de degré non-nul
f
i
:M→N
i
où chaque
N
i
est une variété Haken. Le résultat principal affirme que toute suite (
N
i
,
f
i
) de variétés Haken satisfaisant lim
i→∞
deg(
f
i
)×Vol(
N
i
)=Vol(
M) est finie, à homéomorphisme près. Ce résultat implique en particulier que toute 3-variété close orientable dont le volume simplicial de Gromov est nul (en particulier toute variété graphée) domine au plus un nombre fini de variétés Haken.
Pour citer cet article : P. Derbez, C. R. Acad. Sci. Paris, Ser. I 336 (2003).</description><identifier>ISSN: 1631-073X</identifier><identifier>ISSN: 1778-3569</identifier><identifier>EISSN: 1778-3569</identifier><identifier>DOI: 10.1016/S1631-073X(03)00187-0</identifier><language>eng</language><publisher>Paris: Elsevier SAS</publisher><subject>Exact sciences and technology ; Manifolds and cell complexes ; Mathematics ; Sciences and techniques of general use ; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</subject><ispartof>Comptes rendus. Mathématique, 2003-05, Vol.336 (10), p.833-838</ispartof><rights>2003 Académie des sciences</rights><rights>2003 INIST-CNRS</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c295t-87f7e3e0c84d7ac78ed200251455a413de31608a2103d43f94742bf25f9e11e93</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S1631073X03001870$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3537,27901,27902,65306</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=14843296$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Derbez, P.</creatorcontrib><title>Volume-convergent sequences of Haken 3-manifolds</title><title>Comptes rendus. Mathématique</title><description>Let M be a closed orientable 3-manifold and let Vol(
M) denote its Gromov simplicial volume. This paper is devoted to the study of sequences of non-zero degree maps
f
i
:M→N
i
to Haken manifolds. We prove that any sequence of Haken manifolds (
N
i
,
f
i
), satisfying lim
i→∞
deg(
f
i
)×Vol(
N
i
)=Vol(
M) is finite up to homeomorphism. As an application, we deduce from this fact that any closed orientable 3-manifold with zero Gromov simplicial volume and in particular any graph manifold dominates at most finitely many Haken 3-manifolds.
To cite this article: P. Derbez, C. R. Acad. Sci. Paris, Ser. I 336 (2003).
Soit M une 3-variété close orientable et désignons par Vol(
M) le volume simplicial de Gromov de M. Cette Note est consacrée à l'étude des applications de degré non-nul
f
i
:M→N
i
où chaque
N
i
est une variété Haken. Le résultat principal affirme que toute suite (
N
i
,
f
i
) de variétés Haken satisfaisant lim
i→∞
deg(
f
i
)×Vol(
N
i
)=Vol(
M) est finie, à homéomorphisme près. Ce résultat implique en particulier que toute 3-variété close orientable dont le volume simplicial de Gromov est nul (en particulier toute variété graphée) domine au plus un nombre fini de variétés Haken.
Pour citer cet article : P. Derbez, C. R. Acad. Sci. Paris, Ser. I 336 (2003).</description><subject>Exact sciences and technology</subject><subject>Manifolds and cell complexes</subject><subject>Mathematics</subject><subject>Sciences and techniques of general use</subject><subject>Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</subject><issn>1631-073X</issn><issn>1778-3569</issn><issn>1778-3569</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2003</creationdate><recordtype>article</recordtype><recordid>eNqFkM1LxDAQxYMouK7-CUIvih6iSSZt2pPIoq6w4MEPvIWYTiTaNmvSXfC_t_shHj3NO_xm3rxHyDFnF5zx4vKRF8ApU_B6xuCcMV4qynbIiCtVUsiLanfQv8g-OUjpY4CKSlUjwl5Cs2iR2tAtMb5j12cJvxbYWUxZcNnUfGKXAW1N511o6nRI9pxpEh5t55g83948TaZ09nB3P7meUSuqvKelcgoBmS1lrYxVJdaCMZFzmedGcqgReMFKIziDWoKrpJLizYncVcg5VjAmp5u78xiGf1KvW58sNo3pMCySBqEAlFIDmG9AG0NKEZ2eR9-a-K0506t-9LofvQqvGeh1P4MYk5OtgUnWNC6azvr0tyxLCaIqBu5qw-GQdukx6mT9qp_aR7S9roP_x-kHFnN4QA</recordid><startdate>20030515</startdate><enddate>20030515</enddate><creator>Derbez, P.</creator><general>Elsevier SAS</general><general>Elsevier</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20030515</creationdate><title>Volume-convergent sequences of Haken 3-manifolds</title><author>Derbez, P.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c295t-87f7e3e0c84d7ac78ed200251455a413de31608a2103d43f94742bf25f9e11e93</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2003</creationdate><topic>Exact sciences and technology</topic><topic>Manifolds and cell complexes</topic><topic>Mathematics</topic><topic>Sciences and techniques of general use</topic><topic>Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Derbez, P.</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Comptes rendus. Mathématique</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Derbez, P.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Volume-convergent sequences of Haken 3-manifolds</atitle><jtitle>Comptes rendus. Mathématique</jtitle><date>2003-05-15</date><risdate>2003</risdate><volume>336</volume><issue>10</issue><spage>833</spage><epage>838</epage><pages>833-838</pages><issn>1631-073X</issn><issn>1778-3569</issn><eissn>1778-3569</eissn><abstract>Let M be a closed orientable 3-manifold and let Vol(
M) denote its Gromov simplicial volume. This paper is devoted to the study of sequences of non-zero degree maps
f
i
:M→N
i
to Haken manifolds. We prove that any sequence of Haken manifolds (
N
i
,
f
i
), satisfying lim
i→∞
deg(
f
i
)×Vol(
N
i
)=Vol(
M) is finite up to homeomorphism. As an application, we deduce from this fact that any closed orientable 3-manifold with zero Gromov simplicial volume and in particular any graph manifold dominates at most finitely many Haken 3-manifolds.
To cite this article: P. Derbez, C. R. Acad. Sci. Paris, Ser. I 336 (2003).
Soit M une 3-variété close orientable et désignons par Vol(
M) le volume simplicial de Gromov de M. Cette Note est consacrée à l'étude des applications de degré non-nul
f
i
:M→N
i
où chaque
N
i
est une variété Haken. Le résultat principal affirme que toute suite (
N
i
,
f
i
) de variétés Haken satisfaisant lim
i→∞
deg(
f
i
)×Vol(
N
i
)=Vol(
M) est finie, à homéomorphisme près. Ce résultat implique en particulier que toute 3-variété close orientable dont le volume simplicial de Gromov est nul (en particulier toute variété graphée) domine au plus un nombre fini de variétés Haken.
Pour citer cet article : P. Derbez, C. R. Acad. Sci. Paris, Ser. I 336 (2003).</abstract><cop>Paris</cop><pub>Elsevier SAS</pub><doi>10.1016/S1631-073X(03)00187-0</doi><tpages>6</tpages><oa>free_for_read</oa></addata></record> |
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| source | Elsevier ScienceDirect Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | Exact sciences and technology Manifolds and cell complexes Mathematics Sciences and techniques of general use Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds |
| title | Volume-convergent sequences of Haken 3-manifolds |
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