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Difference between revisions of "Betti group"

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In a broad sense, the same as a [[Homology group|homology group]]; in a narrow sense, the Betti group is the free part of the homology group with as domain of coefficients the group $\mathbf Z$ of integers, if this homology group is finitely generated. Named after E. Betti (1823–1892).
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In a broad sense, the same as a [[homology group]]; in a narrow sense, the Betti group is the free part of the homology group with as domain of coefficients the group $\ZZ$ of integers, if this homology group is finitely generated. Named after E. Betti (1823–1892).
  
 
====References====
 
====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  H. Seifert,  W. Threlfall,  "A textbook of topology" , Acad. Press  (1980)  (Translated from German)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  P.S. Aleksandrov,  "An introduction to homological dimension theory and general combinatorial topology" , Moscow  (1975)  (In Russian)</TD></TR></table>
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<table>
 
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<TR><TD valign="top">[1]</TD> <TD valign="top">  H. Seifert,  W. Threlfall,  "A textbook of topology" , Acad. Press  (1980)  (Translated from German)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  P.S. Aleksandrov,  "An introduction to homological dimension theory and general combinatorial topology" , Moscow  (1975)  (In Russian)</TD></TR>
 
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<TR><TD valign="top">[a1]</TD> <TD valign="top">  E.H. Spanier,  "Algebraic topology" , McGraw-Hill  (1966)</TD></TR>
 
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</table>
====Comments====
 
 
 
 
 
====References====
 
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  E.H. Spanier,  "Algebraic topology" , McGraw-Hill  (1966)</TD></TR></table>
 

Latest revision as of 18:34, 11 April 2023

In a broad sense, the same as a homology group; in a narrow sense, the Betti group is the free part of the homology group with as domain of coefficients the group $\ZZ$ of integers, if this homology group is finitely generated. Named after E. Betti (1823–1892).

References

[1] H. Seifert, W. Threlfall, "A textbook of topology" , Acad. Press (1980) (Translated from German)
[2] P.S. Aleksandrov, "An introduction to homological dimension theory and general combinatorial topology" , Moscow (1975) (In Russian)
[a1] E.H. Spanier, "Algebraic topology" , McGraw-Hill (1966)
How to Cite This Entry:
Betti group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Betti_group&oldid=32657
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article