Geometry & Topology Volume 29, issue 1 (2025)

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

The smooth classification of $4$-dimensional complete intersections

Diarmuid Crowley and Csaba Nagy

Geometry & Topology 29 (2025) 269–311

DOI: 10.2140/gt.2025.29.269

Bibliography

1	J F Adams, On the groups J(X), IV, Topology 5 (1966) 21 MR0198470
2	D Baraglia, The alpha invariant of complete intersections, preprint (2020) arXiv:2002.06750
3	W Browder, Surgery on simply-connected manifolds, 65, Springer (1972) MR0358813
4	W Browder, Complete intersections and the Kervaire invariant, from: "Algebraic topology" (editors J L Dupont, I H Madsen), Lecture Notes in Math. 763, Springer (1979) 88 MR0561215
5	E H Brown Jr., Cohomology theories, Ann. of Math. 75 (1962) 467 MR0138104
6	G Brumfiel, I Madsen, Evaluation of the transfer and the universal surgery classes, Invent. Math. 32 (1976) 133 MR0413099
7	A Dimca, Singularities and topology of hypersurfaces, Springer (1992) MR1194180
8	F Fang, S Klaus, Topological classification of 4-dimensional complete intersections, Manuscripta Math. 90 (1996) 139 MR1391206
9	F Fang, J Wang, Homeomorphism classification of complex projective complete intersections of dimensions 5, 6 and 7, Math. Z. 266 (2010) 719 MR2719429
10	M Feshbach, Essential maps exist from BU to coker J, Proc. Amer. Math. Soc. 97 (1986) 539 MR0840642
11	M Feshbach, The Segal conjecture for compact Lie groups, Topology 26 (1987) 1 MR0880503
12	M H Freedman, The topology of four-dimensional manifolds, J. Differential Geom. 17 (1982) 357 MR0679066
13	V Giambalvo, On ⟨8⟩-cobordism, Illinois J. Math. 15 (1971) 533 MR0287553
14	I Hambleton, I Madsen, Local surgery obstructions and space forms, Math. Z. 193 (1986) 191 MR0856148
15	A Hatcher, Algebraic topology, Cambridge University Press (2002) MR1867354
16	P J Hilton, On the homotopy groups of the union of spheres, J. Lond. Math. Soc. 30 (1955) 154 MR0068218
17	P E Jupp, Classification of certain 6-manifolds, Proc. Cambridge Philos. Soc. 73 (1973) 293 MR0314074
18	R Kasilingam, Classification of smooth structures on a homotopy complex projective space, Proc. Indian Acad. Sci. Math. Sci. 126 (2016) 277 MR3489166
19	M A Kervaire, J W Milnor, Groups of homotopy spheres, I, Ann. of Math. 77 (1963) 504 MR0148075
20	M Kreck, Surgery and duality, Ann. of Math. 149 (1999) 707 MR1709301
21	A S Libgober, J W Wood, Differentiable structures on complete intersections, I, Topology 21 (1982) 469 MR0670748
22	I Madsen, R J Milgram, The classifying spaces for surgery and cobordism of manifolds, 92, Princeton Univ. Press (1979) MR0548575
23	J Milnor, On the Whitehead homomorphism J, Bull. Amer. Math. Soc. 64 (1958) 79 MR0102808
24	J W Milnor, J D Stasheff, Characteristic classes, 76, Princeton Univ. Press (1974) MR0440554
25	R E Mosher, M C Tangora, Cohomology operations and applications in homotopy theory, Harper & Row (1968) MR0226634
26	C Nagy, The classification of 8-dimensional E-manifolds, PhD thesis, University of Melbourne (2021)
27	D C Ravenel, The Segal conjecture for cyclic groups and its consequences, Amer. J. Math. 106 (1984) 415 MR0737779
28	B J Sanderson, Immersions and embeddings of projective spaces, Proc. Lond. Math. Soc. 14 (1964) 137 MR0165532
29	S Smale, On the structure of manifolds, Amer. J. Math. 84 (1962) 387 MR0153022
30	D P Sullivan, Geometric topology : localization, periodicity and Galois symmetry, 8, Springer (1970) MR2162361
31	H Toda, Composition methods in homotopy groups of spheres, 49, Princeton Univ. Press (1962) MR0143217
32	C T C Wall, Classification problems in differential topology, V : On certain 6-manifolds, Invent. Math. 1 (1966) 355 MR0215313
33	C T C Wall, Surgery on compact manifolds, 1, Academic Press (1970) MR431216
34	G W Whitehead, Elements of homotopy theory, 61, Springer (1978) MR0516508