Geometry & Topology Volume 27, issue 2 (2023)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author index

To appear

Other MSP journals

Tautological classes of definite $4$–manifolds

David Baraglia

Geometry & Topology 27 (2023) 641–698

DOI: 10.2140/gt.2023.27.641

Bibliography

1	D Baraglia, Constraints on families of smooth 4–manifolds from Bauer–Furuta invariants, Algebr. Geom. Topol. 21 (2021) 317 MR4224743
2	D Baraglia, H Konno, On the Bauer–Furuta and Seiberg–Witten invariants of families of 4–manifolds, J. Topol. 15 (2022) 505 MR4441598
3	S Bauer, M Furuta, A stable cohomotopy refinement of Seiberg–Witten invariants, I, Invent. Math. 155 (2004) 1 MR2025298
4	M Bustamante, F T Farrell, Y Jiang, Rigidity and characteristic classes of smooth bundles with nonpositively curved fibers, J. Topol. 9 (2016) 934 MR3551844
5	S K Donaldson, An application of gauge theory to four-dimensional topology, J. Differential Geom. 18 (1983) 279 MR710056
6	J Ebert, O Randal-Williams, Generalised Miller–Morita–Mumford classes for block bundles and topological bundles, Algebr. Geom. Topol. 14 (2014) 1181 MR3180831
7	C Faber, A conjectural description of the tautological ring of the moduli space of curves, from: "Moduli of curves and abelian varieties" (editors C Faber, E Looijenga), Aspects Math. E33, Friedr. Vieweg (1999) 109 MR1722541
8	M H Freedman, The topology of four-dimensional manifolds, J. Differential Geometry 17 (1982) 357 MR679066
9	S Galatius, I Grigoriev, O Randal-Williams, Tautological rings for high-dimensional manifolds, Compos. Math. 153 (2017) 851 MR3705243
10	S Galatius, O Randal-Williams, Stable moduli spaces of high-dimensional manifolds, Acta Math. 212 (2014) 257 MR3207759
11	I Grigoriev, Relations among characteristic classes of manifold bundles, Geom. Topol. 21 (2017) 2015 MR3654103
12	A Grothendieck, Le groupe de Brauer, II : Théorie cohomologique, from: "Dix exposés sur la cohomologie des schémas", Adv. Stud. Pure Math. 3, North-Holland (1968) 67 MR244270
13	F Hebestreit, M Land, W Lück, O Randal-Williams, A vanishing theorem for tautological classes of aspherical manifolds, Geom. Topol. 25 (2021) 47 MR4226228
14	E Looijenga, On the tautological ring of ℳ_g, Invent. Math. 121 (1995) 411 MR1346214
15	E Y Miller, The homology of the mapping class group, J. Differential Geom. 24 (1986) 1 MR857372
16	S Morita, Generators for the tautological algebra of the moduli space of curves, Topology 42 (2003) 787 MR1958529
17	C Müller, C Wockel, Equivalences of smooth and continuous principal bundles with infinite-dimensional structure group, Adv. Geom. 9 (2009) 605 MR2574141
18	D Mumford, Towards an enumerative geometry of the moduli space of curves, from: "Arithmetic and geometry, II" (editors M Artin, J Tate), Progr. Math. 36, Birkhäuser (1983) 271 MR717614
19	O Randal-Williams, Some phenomena in tautological rings of manifolds, Selecta Math. 24 (2018) 3835 MR3848035
20	M Szymik, Characteristic cohomotopy classes for families of 4–manifolds, Forum Math. 22 (2010) 509 MR2652709
21	R Thom, Quelques propriétés globales des variétés différentiables, Comment. Math. Helv. 28 (1954) 17 MR61823