The projective-space generation conjecture for isolated fixed-point actions

Let V1,,VkV_1,\ldots,V_k be complex S1S^1-representations, and consider stably complex S1S^1 actions with isolated fixed points. Two weights are relatively prime when their greatest common divisor is one.

Projective-space generation conjecture. Stably complex S1S^1 actions with isolated fixed points up to bordism are generated by linear actions on projective spaces

P(V1V2Vk),\mathbb{P}(V_1\oplus V_2\oplus\cdots\oplus V_k),

where the weights of the ViV_i are relatively prime.

This conjecture proposes that linear projective actions generate the relevant geometric bordism classes. The source points to an example in Theorem 1.6 of Sinha (2000), but does not state that the conjecture has been resolved.

Sources & referencesView supporting material

Primary source

Dev P. Sinha, “Bordism of semi-free S^1 actions”, arXiv:math/0303100 (2004).

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