Algebraic & Geometric Topology Volume 26, issue 7 (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

On lens spaces bounding smooth $4$-manifolds with $b_2=1$

Woohyeok Jo, Jongil Park and Kyungbae Park

Algebraic & Geometric Topology 26 (2026) 2659–2688

DOI: 10.2140/agt.2026.26.2659

Bibliography

1	P Aceto, D McCoy, J Park, Definite fillings of lens spaces, J. Differential Geom. 131 (2025) 1 MR4947548
2	S Akbulut, R Kirby, Mazur manifolds, Michigan Math. J. 26 (1979) 259 MR544597
3	W Ballinger, Configurations of spheres in #ⁿℂP², preprint (2022) arXiv:2209.12851
4	J Berge, Some knots with surgeries yielding lens spaces, preprint (2018) arXiv:1802.09722
5	S Boyer, Simply-connected 4-manifolds with a given boundary, Trans. Amer. Math. Soc. 298 (1986) 331 MR857447
6	A J Casson, J L Harer, Some homology lens spaces which bound rational homology balls, Pacific J. Math. 96 (1981) 23 MR634760
7	S K Donaldson, An application of gauge theory to four-dimensional topology, J. Differential Geom. 18 (1983) 279 MR710056
8	S K Donaldson, The orientation of Yang–Mills moduli spaces and 4-manifold topology, J. Differential Geom. 26 (1987) 397 MR910015
9	S Fukuhara, On an invariant of homology lens spaces, J. Math. Soc. Japan 36 (1984) 259 MR740317
10	R E Gompf, A I Stipsicz, 4-manifolds and Kirby calculus, 20, Amer. Math. Soc. (1999) MR1707327
11	J E Greene, The lens space realization problem, Ann. of Math. 177 (2013) 449 MR3010805
12	J E Greene, L-space surgeries, genus bounds, and the cabling conjecture, J. Differential Geom. 100 (2015) 491 MR3352796
13	D Hwang, J Keum, The maximum number of singular points on rational homology projective planes, J. Algebraic Geom. 20 (2011) 495 MR2786664
14	D Hwang, J Keum, Construction of singular rational surfaces of Picard number one with ample canonical divisor, Proc. Amer. Math. Soc. 140 (2012) 1865 MR2888175
15	D Hwang, J Keum, H Ohashi, Gorenstein ℚ-homology projective planes, Sci. China Math. 58 (2015) 501 MR3319920
16	W Jo, J Park, K Park, On rational homology projective planes with quotient singularities of small indices, preprint (2024) arXiv:2410.22708
17	W Jo, J Park, K Park, Algebraic Montgomery–Yang problem and smooth obstructions, Trans. Amer. Math. Soc. 378 (2025) 2969 MR4880467
18	M A Kervaire, J W Milnor, On 2-spheres in 4-manifolds, Proc. Nat. Acad. Sci. U.S.A. 47 (1961) 1651 MR133134
19	R Kirby, Problems in low-dimensional topology, from: "Geometric topology", AMS/IP Stud. Adv. Math. 2.2, Amer. Math. Soc. (1997) 35 MR1470751
20	H Kojima, Logarithmic del Pezzo surfaces of rank one with unique singular points, Japan. J. Math. 25 (1999) 343 MR1735465
21	J Kollár, Is there a topological Bogomolov–Miyaoka–Yau inequality ?, Pure Appl. Math. Q. 4 (2008) 203 MR2400877
22	Y Lee, J Park, A simply connected surface of general type with p_g = 0 and K² = 2, Invent. Math. 170 (2007) 483 MR2357500
23	P Lisca, Lens spaces, rational balls and the ribbon conjecture, Geom. Topol. 11 (2007) 429 MR2302495
24	M Miyanishi, D Q Zhang, Gorenstein log del Pezzo surfaces of rank one, J. Algebra 118 (1988) 63 MR961326
25	L Moser, Elementary surgery along a torus knot, Pacific J. Math. 38 (1971) 737 MR383406
26	P Ozsváth, Z Szabó, Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary, Adv. Math. 173 (2003) 179 MR1957829
27	J Rasmussen, Lens space surgeries and L-space homology spheres, preprint (2007) arXiv:0710.2531
28	O Saeki, Simply connected 4-manifolds of second Betti number 1 bounded by homology lens spaces, J. Math. Soc. Japan 41 (1989) 593 MR1013069
29	A I Stipsicz, Z Szabó, An exotic smooth structure on ℂℙ²#6ℂℙ², Geom. Topol. 9 (2005) 813 MR2140993
30	M Tange, Homology spheres yielding lens spaces, from: "Proceedings of the Gökova Geometry–Topology Conference 2017" (editors S Akbulut, D Auroux, T Önder), International (2018) 73 MR3838086
31	M Ue, The Fukumoto–Furuta and the Ozsváth–Szabó invariants for spherical 3-manifolds, from: "Algebraic topology: old and new" (editors M Golasiński, Y Rudyak, P Salvatore, N Saveliev, N Wahl), Banach Center Publ. 85, Polish Acad. Sci. Inst. Math. (2009) 121 MR2503523