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Volume 36, Issue 4
Bounding Topology via Geometry, $A$-Simple Fundamental Groups

Xiaochun Rong & Xuchao Yao

DOI: 10.4208/cmr.2020-0030

Commun. Math. Res., 36 (2020), pp. 489-505.

Published online: 2020-11

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  • Abstract

We call a group $A$-simple, if it has no non-trivial normal abelian sub-group. We will present finiteness results in controlled topology via geometry on manifolds whose fundamental groups are $A$-simple.

  • Keywords

$A$-simple fundamental group, collapsing with bounded sectional curvature, finiteness of fundamental groups and diffeomorphic types.

  • AMS Subject Headings

53C21, 53C23, 53C24

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-36-489, author = {Rong , Xiaochun and Yao , Xuchao}, title = {Bounding Topology via Geometry, $A$-Simple Fundamental Groups}, journal = {Communications in Mathematical Research }, year = {2020}, volume = {36}, number = {4}, pages = {489--505}, abstract = {

We call a group $A$-simple, if it has no non-trivial normal abelian sub-group. We will present finiteness results in controlled topology via geometry on manifolds whose fundamental groups are $A$-simple.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2020-0030}, url = {http://global-sci.org/intro/article_detail/cmr/18363.html} }
TY - JOUR T1 - Bounding Topology via Geometry, $A$-Simple Fundamental Groups AU - Rong , Xiaochun AU - Yao , Xuchao JO - Communications in Mathematical Research VL - 4 SP - 489 EP - 505 PY - 2020 DA - 2020/11 SN - 36 DO - http://doi.org/10.4208/cmr.2020-0030 UR - https://global-sci.org/intro/article_detail/cmr/18363.html KW - $A$-simple fundamental group, collapsing with bounded sectional curvature, finiteness of fundamental groups and diffeomorphic types. AB -

We call a group $A$-simple, if it has no non-trivial normal abelian sub-group. We will present finiteness results in controlled topology via geometry on manifolds whose fundamental groups are $A$-simple.

Rong , Xiaochun and Yao , Xuchao. (2020). Bounding Topology via Geometry, $A$-Simple Fundamental Groups. Communications in Mathematical Research . 36 (4). 489-505. doi:10.4208/cmr.2020-0030
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