Euler characteristics of linear symplectic quotients and O(2)-spaces
arxiv(2024)
摘要
We give explicit computations of the Γ-Euler characteristic of several
families of orbit space definable translation groupoids. These include the
translation groupoids associated to finite-dimensional linear representations
of the circle and real and unitary representations of the real 2× 2
orthogonal group. In the case of translation groupoids associated to linear
symplectic quotients of representations of a arbitrary compact Lie group G,
we show that unlike the other cases, the Γ-Euler characteristic depends
only on the group and not on the representation.
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