Halving spaces and lower bounds in real enumerative geometry
Halving spaces and lower bounds in real enumerative geometry
We develop the theory of halving spaces to obtain lower bounds in real enumerative geometry. Halving spaces are topological spaces with an action of a Lie group $\Gamma$ with additional cohomological properties. For $\Gamma=\mathbb{Z}_2$ we recover the conjugation spaces of Hausmann, Holm and Puppe. For $\Gamma=\mathrm{U}(1)$ we obtain the circle …