Path-connectedness of the moduli spaces of metrics with positive isotropic curvature on four-manifolds

Chen, Bing-Long; Huang, Xian-Tao

doi:10.1007/s00208-015-1343-4

Cited by 6 publications

(2 citation statements)

References 34 publications

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“…Especially in recent years there has been intensive activity and substantial further progress on these issues, compare, for example, [2,3,[6][7][8][9][10][11][13][14][15][16][17][18][20][21][22][25][26][27][28][29][30][31][33][34][35][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54]58,60,61,[65][66][67][69]…”

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confidence: 99%

On the topology of moduli spaces of non-negatively curved Riemannian metrics

Tuschmann

Wiemeler

2021

Math. Ann.

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We study spaces and moduli spaces of Riemannian metrics with non-negative Ricci or non-negative sectional curvature on closed and open manifolds. We construct, in particular, the first classes of manifolds for which these moduli spaces have non-trivial rational homotopy, homology and cohomology groups. We also show that in every dimension at least seven (respectively, at least eight) there exist infinite sequences of closed (respectively, open) manifolds of pairwise distinct homotopy type for which the space and moduli space of Riemannian metrics with non-negative sectional curvature has infinitely many path components. A completely analogous statement holds for spaces and moduli spaces of non-negative Ricci curvature metrics.

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confidence: 99%

On the topology of moduli spaces of non-negatively curved Riemannian metrics

Tuschmann

Wiemeler

2021

Math. Ann.

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“…In recent times there has indeed been much activity and progress on these issues, compare, for example, [BB18], [Bel17], [Bel18], [BFK17], [BKS11], [BKS15], [BH15], [BERW17], [BG95], [BG96], [BHSW10], [BWW17], [BFJ16], [Bus16], [Car88], [CH16], [Che04], [CM12], [CS13], [CSS17], [Des17], [DGA19], [DKT18], [FGKO17], [FG16], [FO09], [FO10a], [FO10b], [FS17], [Gaj87], [Goo17], [GL83], [HSS14], [Hit74], [KPT05], [KS93], [LM89], [Loh95], [RS01], [Rub01], [SW19], [TW15], [Tus16], [Wal11], [Wal13], [Wal14], [Wra11], [Wra16],…”

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confidence: 99%

On the topology of moduli spaces of non-negatively curved Riemannian metrics

Tuschmann,

Wiemeler

2017

Preprint

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We study spaces and moduli spaces of Riemannian metrics with nonnegative Ricci or non-negative sectional curvature on closed and open manifolds. We construct, in particular, the first classes of manifolds for which these moduli spaces have non-trivial rational homotopy, homology and cohomology groups. We also show that in every dimension at least seven (respectively, at least eight) there exist infinite sequences of closed (respectively, open) manifolds of pairwise distinct homotopy type for which the space and moduli space of Riemannian metrics with non-negative sectional curvature has infinitely many path components. A completely analogous statement holds for spaces and moduli spaces of non-negative Ricci curvature metrics. * W.T. acknowledges support from DFG Priority Program SPP 2026 'Geometry at Infinity'. † M.W. acknowledges support by DFG Grant HA 3160/11-1 and SFB 878.

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