Difference between revisions of "Euler class"
From Encyclopedia of Mathematics
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The first [[Obstruction|obstruction]] in the construction of sections of a fibration the fibre of which is a sphere, associated with a vector bundle. See [[Characteristic class|Characteristic class]]. | The first [[Obstruction|obstruction]] in the construction of sections of a fibration the fibre of which is a sphere, associated with a vector bundle. See [[Characteristic class|Characteristic class]]. | ||
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| − | Multiplication by the Euler class (sometimes called the orientation class) is one of the homeomorphisms in the Gysin sequence of an oriented sphere bundle [[#References|[a1]]]. The [[Euler characteristic|Euler characteristic]] of a compact, oriented | + | Multiplication by the Euler class (sometimes called the orientation class) is one of the homeomorphisms in the Gysin sequence of an oriented sphere bundle [[#References|[a1]]]. The [[Euler characteristic|Euler characteristic]] of a compact, oriented $n$-dimensional [[Manifold|manifold]] may be calculated from the Euler class of the [[Tangent bundle|tangent bundle]] [[#References|[a1]]], p. 348. |
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<table><TR><TD valign="top">[a1]</TD> <TD valign="top"> E.H. Spanier, "Algebraic topology" , McGraw-Hill (1966) pp. 156</TD></TR></table> | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> E.H. Spanier, "Algebraic topology" , McGraw-Hill (1966) pp. 156</TD></TR></table> | ||
Latest revision as of 18:57, 17 April 2014
The first obstruction in the construction of sections of a fibration the fibre of which is a sphere, associated with a vector bundle. See Characteristic class.
Comments
Multiplication by the Euler class (sometimes called the orientation class) is one of the homeomorphisms in the Gysin sequence of an oriented sphere bundle [a1]. The Euler characteristic of a compact, oriented $n$-dimensional manifold may be calculated from the Euler class of the tangent bundle [a1], p. 348.
References
| [a1] | E.H. Spanier, "Algebraic topology" , McGraw-Hill (1966) pp. 156 |
How to Cite This Entry:
Euler class. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Euler_class&oldid=31830
Euler class. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Euler_class&oldid=31830
This article was adapted from an original article by A.F. Kharshiladze (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article