Algebraic & Geometric Topology Volume 26, issue 4 (2026)

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On embeddings of $4$-manifolds in codimension $2$

Abhijeet Ghanwat and Dishant M Pancholi

Algebraic & Geometric Topology 26 (2026) 1293–1320

DOI: 10.2140/agt.2026.26.1293

Bibliography

1	D Auroux, S K Donaldson, L Katzarkov, Singular Lefschetz pencils, Geom. Topol. 9 (2005) 1043 MR2140998
2	W P Barth, K Hulek, C A M Peters, A Van de Ven, Compact complex surfaces, 4, Springer (2004) MR2030225
3	R İ Baykur, Existence of broken Lefschetz fibrations, Int. Math. Res. Not. 2008 (2008) MR2439543
4	R İ Baykur, Topology of broken Lefschetz fibrations and near-symplectic four-manifolds, Pacific J. Math. 240 (2009) 201 MR2485463
5	R İ Baykur, O Saeki, Simplified broken Lefschetz fibrations and trisections of 4-manifolds, Proc. Natl. Acad. Sci. USA 115 (2018) 10894 MR3871793
6	R İ Baykur, O Saeki, Simplifying indefinite fibrations on 4-manifolds, Trans. Amer. Math. Soc. 376 (2023) 3011 MR4577327
7	S E Cappell, J L Shaneson, Embeddings and immersions of four-dimensional manifolds in ℝ⁶, from: "Geometric topology" (editor J C Cantrell), Academic (1979) 301 MR537736
8	M Dehn, Die Gruppe der Abbildungsklassen : das arithmetische Feld auf Flächen, Acta Math. 69 (1938) 135 MR1555438
9	S K Donaldson, Symplectic submanifolds and almost-complex geometry, J. Differential Geom. 44 (1996) 666 MR1438190
10	S K Donaldson, Lefschetz pencils on symplectic manifolds, J. Differential Geom. 53 (1999) 205 MR1802722
11	C J Earle, J Eells, The diffeomorphism group of a compact Riemann surface, Bull. Amer. Math. Soc. 73 (1967) 557 MR212840
12	B Farb, D Margalit, A primer on mapping class groups, 49, Princeton Univ. Press (2012) MR2850125
13	D T Gay, R Kirby, Constructing Lefschetz-type fibrations on four-manifolds, Geom. Topol. 11 (2007) 2075 MR2350472
14	R E Gompf, A I Stipsicz, 4-manifolds and Kirby calculus, 20, Amer. Math. Soc. (1999) MR1707327
15	P Griffiths, J Harris, Principles of algebraic geometry, Wiley (1994) MR1288523
16	A Haefliger, Plongements différentiables dans le domaine stable, Comment. Math. Helv. 37 (1962/63) 155 MR157391
17	A Haefliger, M W Hirsch, On the existence and classification of differentiable embeddings, Topology 2 (1963) 129 MR149494
18	S Hirose, A Yasuhara, Surfaces in 4-manifolds and their mapping class groups, Topology 47 (2008) 41 MR2415773
19	M W Hirsch, On imbedding differentiable manifolds in euclidean space, Ann. of Math. (2) 73 (1961) 566 MR124915
20	M W Hirsch, On embedding 4-manifolds in R⁷, Proc. Cambridge Philos. Soc. 61 (1965) 657 MR182980
21	W B R Lickorish, A representation of orientable combinatorial 3-manifolds, Ann. of Math. (2) 76 (1962) 531 MR151948
22	W B R Lickorish, A finite set of generators for the homeotopy group of a 2-manifold, Proc. Cambridge Philos. Soc. 60 (1964) 769 MR171269
23	W S Massey, F P Peterson, On the dual Stiefel–Whitney classes of a manifold, Bol. Soc. Mat. Mexicana (2) 8 (1963) 1 MR163325
24	D M Pancholi, S Pandit, K Saha, Embeddings of 3-manifolds via open books, J. Ramanujan Math. Soc. 36 (2021) 243 MR4328137
25	V A Rohlin, The embedding of non-orientable three-manifolds into five-dimensional Euclidean space, Dokl. Akad. Nauk SSSR 160 (1965) 549 MR184246
26	D Ruberman, Imbedding four-manifolds and slicing links, Math. Proc. Cambridge Philos. Soc. 91 (1982) 107 MR633261
27	C T C Wall, All 3-manifolds imbed in 5-space, Bull. Amer. Math. Soc. 71 (1965) 564 MR175139