On the o-minimal LS-category

2009/05/09 by Baro, Elias
#03C64 #14P10 #55M30 #55Q99 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.0905.1391

Abstract

We introduce the o-minimal LS-category of definable sets in o-minimal expansions of ordered fields and we establish a relation with the semialgebraic and the classical one. We also study the o-minimal LS-category of definable groups. Along the way, we show that two definably connected definably compact definable groups G and H are definable homotopy equivalent if and only if L(G) and L(H) are homotopy equivalent, where L is the functor which associates to each definable group its corresponding Lie group via Pillay's conjecture.

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