Euler characteristics of linear symplectic quotients and O(2)-spaces
Carla Farsi, Hannah Meit, and Christopher Seaton
Journal of Singularities
volume 28 (2025), 1-22
Received: 5 March 2024. In revised form: 6 December 2024
Abstract:
We give explicit computations of the Gamma-Euler characteristic for 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 2x2 orthogonal group. In the case of translation groupoids associated to linear symplectic quotients of representations of an arbitrary compact Lie group G, we show that unlike the other cases, the Gamma-Euler characteristic depends only on the group and not on the representation.
2020 Mathematical Subject Classification:
Primary 57S15; Secondary 22A22, 14P10, 57R18
Key words and phrases:
definable Euler characteristic, circle-representation, O(2)-representation, symplectic quotient, orbit space definable groupoid.
Author(s) information:
Carla Farsi
Department of Mathematics
University of Colorado at Boulder
UCB 395
Boulder, CO 80309-0395
email: farsi@euclid.colorado.edu
Hannah Meit
Department of Mathematics and Statistics
Rhodes College
2000 N. Parkway
Memphis, TN 38112
email: meihe-25@rhodes.edu
Christopher Seaton
Department of Mathematics and Statistics
Rhodes College
2000 N. Parkway
Memphis, TN 38112
current address:
Department of Mathematics and Statistics
Skidmore College
815 North Broadway
Saratoga Springs, NY 12866, USA
email: cseaton@skidmore.edu