Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
Several popular ways of writing down the tautogical line bundle $\mathcal{L}$ over some projective space donâ€™t generalize, say to the equivariant context.
This here is better, it seems:
$\array{ \mathcal{L}_v & \coloneqq & \frac{ (V \setminus \{0\}) \times k^\ast }{ k^\times } & \overset{ [v,z] \mapsto \big( [v], v \cdot z \big) }{\hookrightarrow} & \frac{ V \setminus \{0\} }{ k^\times } \times V \\ \big\downarrow && \big\downarrow {}^{\mathrlap{ \frac{id \times pt}{ k^\times } }} \\ k P(V) &=& \frac{ (V \setminus \{0\}) \times \ast }{ k^\times } }$In this notation, is it correct that the virtual equivariant line bundle which gives Bott periodicity for complex equivariant K-theory with respect to a complex 1d representation $V$ is $\mathcal{L}_{1 \oplus V} - 1$?
1 to 2 of 2