Equivariant vector fields and self-maps of spheres
Costenoble, Steven R. and Waner, Stefan (2002) Equivariant vector fields and self-maps of spheres. Steven R. Costenoble.
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We identify, for actions of a compact Lie group, the generalization of the Euler characteristic that is the sole obstruction to the existence of a nowhere-zero smooth equivariant tangent vector field. We use this characteristic to calculate the monoid of self-maps of the unit sphere of a representation. We also generalize the construction of the stable fundamental groupoid for use in future work.
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