p-Group Actions on Homology Spheres

Ronald M. Dotzel; Gary C. Hamrick

doi:10.1007/BF01394253

p-Group Actions on Homology Spheres

Research output: Contribution to journal › Article › peer-review

Abstract

<div class="line" id="line-7"> When an arbitraryp-groupG acts on a &integers; n -homologyn-sphereX, it is proved here that the dimension functionn:S(G)→&integers;(S(G) is the set of subgroups ofG), defined byn(H)=dimXH, (dim here is cohomological dimension) is realised by a real representation ofG, and that there is an equivariant map fromX to the sphere of this representation. A converse is also established.</div>

Original language	American English
Journal	Inventiones Mathematicae
Volume	62
DOIs	https://doi.org/10.1007/BF01394253
State	Published - Jan 10 1980
Externally published	Yes

Disciplines

Analysis
Mathematics

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abstract = " When an arbitraryp-groupG acts on a \&integers; n -homologyn-sphereX, it is proved here that the dimension functionn:S(G)\→\&integers;(S(G) is the set of subgroups ofG), defined byn(H)=dimXH, (dim here is cohomological dimension) is realised by a real representation ofG, and that there is an equivariant map fromX to the sphere of this representation. A converse is also established.",

author = "Dotzel, \{Ronald M.\} and Hamrick, \{Gary C.\}",

note = "When an arbitrary p-group G acts on a ℤ n-homology n-sphere X, it is proved here that the dimension function n: S( G)→ℤ( S( G) is the set of subgroups of G), defined by n(H)=dim XH, (dim here is...",

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doi = "10.1007/BF01394253",

language = "American English",

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journal = "Inventiones Mathematicae",

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T1 - p-Group Actions on Homology Spheres

AU - Dotzel, Ronald M.

AU - Hamrick, Gary C.

N1 - When an arbitrary p-group G acts on a ℤ n-homology n-sphere X, it is proved here that the dimension function n: S( G)→ℤ( S( G) is the set of subgroups of G), defined by n(H)=dim XH, (dim here is...

PY - 1980/1/10

Y1 - 1980/1/10

N2 - When an arbitraryp-groupG acts on a &integers; n -homologyn-sphereX, it is proved here that the dimension functionn:S(G)→&integers;(S(G) is the set of subgroups ofG), defined byn(H)=dimXH, (dim here is cohomological dimension) is realised by a real representation ofG, and that there is an equivariant map fromX to the sphere of this representation. A converse is also established.

AB - When an arbitraryp-groupG acts on a &integers; n -homologyn-sphereX, it is proved here that the dimension functionn:S(G)→&integers;(S(G) is the set of subgroups ofG), defined byn(H)=dimXH, (dim here is cohomological dimension) is realised by a real representation ofG, and that there is an equivariant map fromX to the sphere of this representation. A converse is also established.

UR - https://link.springer.com/article/10.1007%2FBF01394253

U2 - 10.1007/BF01394253

DO - 10.1007/BF01394253

M3 - Article

VL - 62

JO - Inventiones Mathematicae

JF - Inventiones Mathematicae

ER -

p-Group Actions on Homology Spheres

Abstract

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