Algebraic & Geometric Topology Volume 26, issue 2 (2026)

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): 1472-2739

ISSN (print): 1472-2747

Author index

To appear

Other MSP journals

Explicit formulas for the Hattori–Stong theorem and applications

Ping Li and Wangyang Lin

Algebraic & Geometric Topology 26 (2026) 735–750

DOI: 10.2140/agt.2026.26.735

Bibliography

1	J F Adams, On the non-existence of elements of Hopf invariant one, Ann. of Math. (2) 72 (1960) 20 MR141119
2	J Adem, The iteration of the Steenrod squares in algebraic topology, Proc. Nat. Acad. Sci. U.S.A. 38 (1952) 720 MR50278
3	M F Atiyah, K-theory, W. A. Benjamin (1967) MR224083
4	M F Atiyah, F Hirzebruch, Riemann–Roch theorems for differentiable manifolds, Bull. Amer. Math. Soc. 65 (1959) 276 MR110106
5	M F Atiyah, F Hirzebruch, Cohomologie-Operationen und charakteristische Klassen, Math. Z. 77 (1961) 149 MR156361
6	M F Atiyah, I M Singer, The index of elliptic operators, III, Ann. of Math. (2) 87 (1968) 546 MR236952
7	J Barge, Structures différentiables sur les types d’homotopie rationnelle simplement connexes, Ann. Sci. École Norm. Sup. (4) 9 (1976) 469 MR440574
8	A Berglund, J Bergström, Hirzebruch L-polynomials and multiple zeta values, Math. Ann. 372 (2018) 125 MR3856808
9	A Borel, J P Serre, Groupes de Lie et puissances réduites de Steenrod, Amer. J. Math. 75 (1953) 409 MR58213
10	P Doubilet, On the foundations of combinatorial theory, VII : Symmetric functions through the theory of distribution and occupancy, Studies in Appl. Math. 51 (1972) 377 MR429577
11	J Fowler, Z Su, Smooth manifolds with prescribed rational cohomology ring, Geom. Dedicata 182 (2016) 215 MR3500384
12	A Hattori, Integral characteristic numbers for weakly almost complex manifolds, Topology 5 (1966) 259 MR192517
13	F Hirzebruch, Some problems on differentiable and complex manifolds, Ann. of Math. (2) 60 (1954) 213 MR66013
14	F Hirzebruch, Topological methods in algebraic geometry, 131, Springer (1966) MR202713
15	F Hirzebruch, Gesammelte Abhandlungen - Collected papers, I : 1951–1962, Springer (2013) MR3184395
16	F Hirzebruch, Gesammelte Abhandlungen - Collected papers, II : 1963–1987, Springer (2013) MR3184930
17	F Hirzebruch, The index of an oriented manifold and the Todd genus of an almost complex manifold, from: "Gesammelte Abhandlungen - Collected papers, I : 1951–1962", Springer (2013) 60
18	F Hirzebruch, On the characteristic cohomology classes of differentiable manifolds, from: "Gesammelte Abhandlungen - Collected papers, I : 1951–1962", Springer (2013) 145
19	F Hirzebruch, T Berger, R Jung, Manifolds and modular forms, E20, Vieweg & Sohn (1992) MR1189136
20	J Hu, Almost complex manifolds with total Betti number three, J. Topol. Anal. 16 (2024) 945 MR4790651
21	P J Kahn, Obstructions to extending almost X-structures, Illinois J. Math. 13 (1969) 336 MR258037
22	M Karoubi, K-theory : an introduction, 226, Springer (1978) MR488029
23	L Kennard, Z Su, On dimensions supporting a rational projective plane, J. Topol. Anal. 11 (2019) 535 MR3999512
24	P Li, The complex genera, symmetric functions and multiple zeta values, J. Combin. Theory Ser. A 206 (2024) 105893 MR4727642
25	I G Macdonald, Symmetric functions and Hall polynomials, Oxford Univ. Press (1995) MR1354144
26	A Milivojević, On the characterization of rational homotopy types and Chern classes of closed almost complex manifolds, Complex Manifolds 9 (2022) 138 MR4416922
27	J Milnor, On the cobordism ring Ω^∗ and a complex analogue, I, Amer. J. Math. 82 (1960) 505 MR119209
28	J W Milnor, J D Stasheff, Characteristic classes, 76, Princeton Univ. Press (1974) MR440554
29	V H Moll, Numbers and functions : from a classical-experimental mathematician’s point of view, 65, Amer. Math. Soc. (2012) MR2963308
30	C Rovi, S Yokura, Hirzebruch χ_y-genera modulo 8 of fiber bundles for odd integers y, Pure Appl. Math. Q. 12 (2016) 587 MR3842855
31	R P Stanley, Enumerative combinatorics, I, 49, Cambridge Univ. Press (1997) MR1442260
32	R P Stanley, Enumerative combinatorics, II, 62, Cambridge Univ. Press (1999) MR1676282
33	R E Stong, Relations among characteristic numbers, I, Topology 4 (1965) 267 MR192515
34	R E Stong, Relations among characteristic numbers, II, Topology 5 (1966) 133 MR192516
35	R E Stong, Notes on cobordism theory, Princeton Univ. Press (1968) MR248858
36	Z Su, Rational homotopy type of manifolds, PhD thesis, Indiana University (2009) MR2717838
37	Z Su, Rational analogs of projective planes, Algebr. Geom. Topol. 14 (2014) 421 MR3158765
38	Z Su, Almost complex manifold with Betti number b_i = 0 except i = 0,n∕2,n, (2022) arXiv:2204.04800
39	D Sullivan, Infinitesimal computations in topology, Inst. Hautes Études Sci. Publ. Math. 47 (1977) 269 MR646078