Weak coherence of groups and finite decomposition complexity
The weak regular coherence is a coarse property of a finitely generated group $\Gamma$. It was introduced by G. Carlsson and this author to play the role of a weakening of Waldhausen's regular coherence as part of computation of the integral K-theoretic assembly map. A new class of metric space...
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| creator | Goldfarb, Boris |
| description | The weak regular coherence is a coarse property of a finitely generated group
$\Gamma$. It was introduced by G. Carlsson and this author to play the role of
a weakening of Waldhausen's regular coherence as part of computation of the
integral K-theoretic assembly map. A new class of metric spaces (sFDC) was
introduced recently by A. Dranishnikov and M. Zarichnyi. This class includes
most notably the spaces with finite decomposition complexity (FDC) studied by
E. Guentner, D. Ramras, R. Tessera, and G. Yu. The main theorem of this paper
shows that a group that has finite $K(\Gamma,1)$ and sFDC is weakly regular
coherent. As a consequence, the integral K-theoretic assembly maps are
isomorphisms in all dimensions for any group that has finite $K(\Gamma,1)$ and
FDC. In particular, the Whitehead group $Wh (\Gamma)$ is trivial for such
groups. |
| doi_str_mv | 10.48550/arxiv.1307.5345 |
| format | Article |
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$\Gamma$. It was introduced by G. Carlsson and this author to play the role of
a weakening of Waldhausen's regular coherence as part of computation of the
integral K-theoretic assembly map. A new class of metric spaces (sFDC) was
introduced recently by A. Dranishnikov and M. Zarichnyi. This class includes
most notably the spaces with finite decomposition complexity (FDC) studied by
E. Guentner, D. Ramras, R. Tessera, and G. Yu. The main theorem of this paper
shows that a group that has finite $K(\Gamma,1)$ and sFDC is weakly regular
coherent. As a consequence, the integral K-theoretic assembly maps are
isomorphisms in all dimensions for any group that has finite $K(\Gamma,1)$ and
FDC. In particular, the Whitehead group $Wh (\Gamma)$ is trivial for such
groups.</description><identifier>DOI: 10.48550/arxiv.1307.5345</identifier><language>eng</language><subject>Mathematics - Geometric Topology ; Mathematics - Group Theory ; Mathematics - K-Theory and Homology</subject><creationdate>2013-07</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,781,886</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1307.5345$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1307.5345$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Goldfarb, Boris</creatorcontrib><title>Weak coherence of groups and finite decomposition complexity</title><description>The weak regular coherence is a coarse property of a finitely generated group
$\Gamma$. It was introduced by G. Carlsson and this author to play the role of
a weakening of Waldhausen's regular coherence as part of computation of the
integral K-theoretic assembly map. A new class of metric spaces (sFDC) was
introduced recently by A. Dranishnikov and M. Zarichnyi. This class includes
most notably the spaces with finite decomposition complexity (FDC) studied by
E. Guentner, D. Ramras, R. Tessera, and G. Yu. The main theorem of this paper
shows that a group that has finite $K(\Gamma,1)$ and sFDC is weakly regular
coherent. As a consequence, the integral K-theoretic assembly maps are
isomorphisms in all dimensions for any group that has finite $K(\Gamma,1)$ and
FDC. In particular, the Whitehead group $Wh (\Gamma)$ is trivial for such
groups.</description><subject>Mathematics - Geometric Topology</subject><subject>Mathematics - Group Theory</subject><subject>Mathematics - K-Theory and Homology</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj8tqwzAURLXJoqTdd1X0A3b1urIM3YTQRyDQTaBLc_VqRBLLyG5J_r512tUMDBzmEHLPWa0MAHvEck7fNZesqUEquCFPHwEP1OV9KKF3geZIP0v-GkaKvacx9WkK1AeXT0Me05RyT-d-DOc0XW7JIuJxDHf_uSS7l-fd-q3avr9u1qtthRqgapiSwQpjELyOYLSxEaX1zHiuhPDcuaaNVvjf2TpokUctpG-VdVKjsnJJHv6w1_fdUNIJy6WbLbrZQv4AwIZC7w</recordid><startdate>20130719</startdate><enddate>20130719</enddate><creator>Goldfarb, Boris</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20130719</creationdate><title>Weak coherence of groups and finite decomposition complexity</title><author>Goldfarb, Boris</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a655-7043eb288a5d6f5868bfa3bd08d1422d1cc79fb2d5d6bc59a1f623d94bc36a4b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Mathematics - Geometric Topology</topic><topic>Mathematics - Group Theory</topic><topic>Mathematics - K-Theory and Homology</topic><toplevel>online_resources</toplevel><creatorcontrib>Goldfarb, Boris</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Goldfarb, Boris</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Weak coherence of groups and finite decomposition complexity</atitle><date>2013-07-19</date><risdate>2013</risdate><abstract>The weak regular coherence is a coarse property of a finitely generated group
$\Gamma$. It was introduced by G. Carlsson and this author to play the role of
a weakening of Waldhausen's regular coherence as part of computation of the
integral K-theoretic assembly map. A new class of metric spaces (sFDC) was
introduced recently by A. Dranishnikov and M. Zarichnyi. This class includes
most notably the spaces with finite decomposition complexity (FDC) studied by
E. Guentner, D. Ramras, R. Tessera, and G. Yu. The main theorem of this paper
shows that a group that has finite $K(\Gamma,1)$ and sFDC is weakly regular
coherent. As a consequence, the integral K-theoretic assembly maps are
isomorphisms in all dimensions for any group that has finite $K(\Gamma,1)$ and
FDC. In particular, the Whitehead group $Wh (\Gamma)$ is trivial for such
groups.</abstract><doi>10.48550/arxiv.1307.5345</doi><oa>free_for_read</oa></addata></record> |
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| language | eng |
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| subjects | Mathematics - Geometric Topology Mathematics - Group Theory Mathematics - K-Theory and Homology |
| title | Weak coherence of groups and finite decomposition complexity |
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