Difference between revisions of "Betti group"
From Encyclopedia of Mathematics
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| − | In a broad sense, the same as a [[ | + | 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> |
| − | + | <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> | |
| − | + | <TR><TD valign="top">[a1]</TD> <TD valign="top"> E.H. Spanier, "Algebraic topology" , McGraw-Hill (1966)</TD></TR> | |
| − | + | </table> | |
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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
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