# On the homeomorphism groups of manifolds and their universal coverings

Agnieszka Kowalik; Tomasz Rybicki

Open Mathematics (2011)

- Volume: 9, Issue: 6, page 1217-1231
- ISSN: 2391-5455

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topAgnieszka Kowalik, and Tomasz Rybicki. "On the homeomorphism groups of manifolds and their universal coverings." Open Mathematics 9.6 (2011): 1217-1231. <http://eudml.org/doc/269639>.

@article{AgnieszkaKowalik2011,

abstract = {Let H c(M) stand for the path connected identity component of the group of all compactly supported homeomorphisms of a manifold M. It is shown that H c(M) is perfect and simple under mild assumptions on M. Next, conjugation-invariant norms on Hc(M) are considered and the boundedness of Hc(M) and its subgroups is investigated. Finally, the structure of the universal covering group of Hc(M) is studied.},

author = {Agnieszka Kowalik, Tomasz Rybicki},

journal = {Open Mathematics},

keywords = {Group of homeomorphisms; Universal covering group; Perfect group; Bounded group; Fragmentation; Isotopy; group of homeomorphisms; universal covering group; perfect group; bounded group; fragmentation; isotopy},

language = {eng},

number = {6},

pages = {1217-1231},

title = {On the homeomorphism groups of manifolds and their universal coverings},

url = {http://eudml.org/doc/269639},

volume = {9},

year = {2011},

}

TY - JOUR

AU - Agnieszka Kowalik

AU - Tomasz Rybicki

TI - On the homeomorphism groups of manifolds and their universal coverings

JO - Open Mathematics

PY - 2011

VL - 9

IS - 6

SP - 1217

EP - 1231

AB - Let H c(M) stand for the path connected identity component of the group of all compactly supported homeomorphisms of a manifold M. It is shown that H c(M) is perfect and simple under mild assumptions on M. Next, conjugation-invariant norms on Hc(M) are considered and the boundedness of Hc(M) and its subgroups is investigated. Finally, the structure of the universal covering group of Hc(M) is studied.

LA - eng

KW - Group of homeomorphisms; Universal covering group; Perfect group; Bounded group; Fragmentation; Isotopy; group of homeomorphisms; universal covering group; perfect group; bounded group; fragmentation; isotopy

UR - http://eudml.org/doc/269639

ER -

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