Nontriviality of the spin^c index difference homomorphism

From papers

Let (M,L)(M,L) be a closed spinc^c non-spin manifold with dimM5\dim M\geq 5 and with Rgen+(M,L)\mathcal R^{{\mathrm{gen}+}}(M,L)\neq\emptyset. Fix a basepoint (g0,A0)Rgen+(M,L)(g_0,A_0)\in\mathcal R^{{\mathrm{gen}+}}(M,L), and let

inddiffc(M,L) ⁣:πq(Rgen+(M,L))KUq+n+1\operatorname{inddiff}^c(M,L)\colon \pi_q(\mathcal R^{{\mathrm{gen}+}}(M,L))\to KU_{q+n+1}

be the spinc^c index difference homomorphism. The spinc^c index difference conjecture. The homomorphism inddiffc(M,L)\operatorname{inddiff}^c(M,L) is non-trivial if the target group KUq+n+1KU_{q+n+1} is non-zero.

This proposes a spinc^c analogue of the nontriviality result for the index difference homomorphism on spaces of positive scalar curvature metrics. The parser supplies no evidence that the claim has been proved or disproved.

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Sources & referencesView supporting material

Primary source

Boris Botvinnik and Jonathan Rosenberg, “Generalized positive scalar curvature on spin^c manifolds”, arXiv:2404.00703 (2024).

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