DOI QR코드

DOI QR Code

SEMIALGEBRAIC ORBIT STRUCTURES

  • Dae Heui Park (Department of Mathematics Chonnam National University)
  • Received : 2023.11.01
  • Accepted : 2023.11.21
  • Published : 2023.11.30

Abstract

Let G be a semialgebraic group not necessarily compact. In this paper, we prove that the orbit space of every proper semialgebraic G-set has a semialgebraic structure.

Keywords

References

  1. J. Bochnak, M. Coste, and M.-F. Roy, Real Agebraic Geometry, 36 of Erg. der Math. und ihrer Grenzg, Springer-Verlag, Berlin Heidelberg, 1998.
  2. G. W. Brumfiel, Quotient space for semialgebraic equivalence relation, Math. Z., 195 (1987), 69-78. https://doi.org/10.1007/BF01161599
  3. H. Delfs and M. Knebusch, Locally Semialgebraic Spaces, volume 1173 of Lecture Notes in Math., Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1985.
  4. V. Guillemin, V. Ginzburg, and Y. Karshon, Moment maps, cobordisms, and hamiltonian group actions, volume 98 of Mathematical surveys and monographs., Amer. Math. Soc., 1998.
  5. D. Montgomery and L. Zippin, A theorem on Lie groups, Bull. Amer. Math. Soc., 8 (1942), 448-452. https://doi.org/10.1090/S0002-9904-1942-07699-3
  6. R. S. Palais, On the existence of slices for actions of non-compact Lie groups, Ann. of Math., 73 (1961), no. 2, 295-323. https://doi.org/10.2307/1970335
  7. D. H. Park, A note on semialgebraically proper maps, Ukrainian Math. J., 66 (2015), no. 9, 1414-1422. https://doi.org/10.1007/s11253-015-1020-5
  8. D. H. Park, Equivariant semialgebraic embeddings, J. Chungcheong Math. Soc., 35 (2022), no. 1, 13-23.
  9. A. Pillay, On groups and fields definable in o-minimal structures, J. Pure Applied Algebra 53 (1988), 239-255. https://doi.org/10.1016/0022-4049(88)90125-9
  10. C. Scheiderer, Quotients of semi-algebraic spaces, Math. Z., 201 (1989), 249-271. https://doi.org/10.1007/BF01160681