14 citations · 42 across the 17 of their papers we have counts for
4 papers · 1 filter
Connected components of definable groups, and o-minimality II
Annalisa Conversano, Anand Pillay
We study the connected components G^00, G^000 and their quotients for a group G definable in a saturated o-minimal expansion of a real closed field. We show that G^00/G^000 is natu…
Affine Nash groups over real closed fields
Ehud Hrushovski, Anand Pillay
We prove that a semialgebraically connected affine Nash group over a real closed field R is Nash isogenous to the semialgebraically connected component of the group H(R) of R-point…
Connected components of definable groups and o-minimality I
Annalisa Conversano, Anand Pillay
We give examples of groups G such that G^00 is different from G^000. We also prove that for groups G definable in an o-minimal structure, G has a "bounded orbit" iff G is definably…
Groups definable in o-minimal structures: structure theorem, G^000, definable amenability and bounded orbits
Anand Pillay
We settle some open problems in the special case of groups in o-minimal structures, such as the equality of G^00 and G^000 and the equivalence of definable amenability and existenc…