Geometry & Topology Volume 28, issue 4 (2024)

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

On definite lattices bounded by a homology $3$–sphere and Yang–Mills instanton Floer theory

Christopher Scaduto

Geometry & Topology 28 (2024) 1587–1628

DOI: 10.2140/gt.2024.28.1587

Bibliography

1	S Akbulut, T Mrowka, Y Ruan, Torsion classes and a universal constraint on Donaldson invariants for odd manifolds, Trans. Amer. Math. Soc. 347 (1995) 63 MR1270658
2	M F Atiyah, R Bott, The Yang–Mills equations over Riemann surfaces, Philos. Trans. Roy. Soc. Lond. Ser. A 308 (1983) 523 MR702806
3	S Behrens, M Golla, Heegaard Floer correction terms, with a twist, Quantum Topol. 9 (2018) 1 MR3760877
4	P J Braam, S K Donaldson, Floer’s work on instanton homology, knots and surgery, from: "The Floer memorial volume" (editors H Hofer, C H Taubes, A Weinstein, E Zehnder), Progr. Math. 133, Birkhäuser (1995) 195 MR1362829
5	T D Cochran, R E Gompf, Applications of Donaldson’s theorems to classical knot concordance, homology 3–spheres and property P, Topology 27 (1988) 495 MR976591
6	J H Conway, N J A Sloane, On the enumeration of lattices of determinant one, J. Number Theory 15 (1982) 83 MR666350
7	J H Conway, N J A Sloane, Sphere packings, lattices and groups, 290, Springer (1999) MR1662447
8	S K Donaldson, Connections, cohomology and the intersection forms of 4–manifolds, J. Differential Geom. 24 (1986) 275 MR868974
9	S K Donaldson, The orientation of Yang–Mills moduli spaces and 4–manifold topology, J. Differential Geom. 26 (1987) 397 MR0910015
10	S K Donaldson, Floer homology groups in Yang–Mills theory, 147, Cambridge Univ. Press (2002) MR1883043
11	S K Donaldson, P B Kronheimer, The geometry of four-manifolds, Oxford Univ. Press (1990) MR1079726
12	W Ebeling, Lattices and codes, Vieweg & Sohn (1994) MR1280458
13	N D Elkies, A characterization of the ℤⁿ lattice, Math. Res. Lett. 2 (1995) 321 MR1338791
14	N D Elkies, Lattices and codes with long shadows, Math. Res. Lett. 2 (1995) 643 MR1359968
15	R Fintushel, R J Stern, Definite 4–manifolds, J. Differential Geom. 28 (1988) 133 MR950558
16	R Fintushel, R J Stern, Instanton homology of Seifert fibred homology three spheres, Proc. Lond. Math. Soc. 61 (1990) 109 MR1051101
17	R Fintushel, R Stern, The canonical class of a symplectic 4–manifold, Turkish J. Math. 25 (2001) 137 MR1829084
18	A Floer, An instanton-invariant for 3–manifolds, Comm. Math. Phys. 118 (1988) 215 MR956166
19	A Floer, Instanton homology and Dehn surgery, from: "The Floer memorial volume" (editors H Hofer, C H Taubes, A Weinstein, E Zehnder), Progr. Math. 133, Birkhäuser (1995) 77 MR1362823
20	K A Frøyshov, On Floer homology and four-manifolds with boundary, PhD thesis, University of Oxford (1995)
21	K A Frøyshov, Equivariant aspects of Yang–Mills Floer theory, Topology 41 (2002) 525 MR1910040
22	K A Frøyshov, An inequality for the h–invariant in instanton Floer theory, Topology 43 (2004) 407 MR2052970
23	K A Frøyshov, Monopole Floer homology for rational homology 3–spheres, Duke Math. J. 155 (2010) 519 MR2738582
24	K Fukaya, Floer homology of connected sum of homology 3–spheres, Topology 35 (1996) 89 MR1367277
25	M Furuta, Homology cobordism group of homology 3–spheres, Invent. Math. 100 (1990) 339 MR1047138
26	M Golla, C Scaduto, On definite lattices bounded by integer surgeries along knots with slice genus at most 2, Trans. Amer. Math. Soc. 372 (2019) 7805 MR4029682
27	P B Kronheimer, T S Mrowka, Embedded surfaces and the structure of Donaldson’s polynomial invariants, J. Differential Geom. 41 (1995) 573 MR1338483
28	V Muñoz, Ring structure of the Floer cohomology of Σ × 𝕊¹, Topology 38 (1999) 517 MR1670396
29	Y Ni, Z Wu, Cosmetic surgeries on knots in S³, J. Reine Angew. Math. 706 (2015) 1 MR3393360
30	P Ozsváth, Z Szabó, Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary, Adv. Math. 173 (2003) 179 MR1957829
31	J Rasmussen, Lens space surgeries and a conjecture of Goda and Teragaito, Geom. Topol. 8 (2004) 1013 MR2087076
32	C Scaduto, M Stoffregen, The cohomology of rank two stable bundle moduli: mod two nilpotency and skew Schur polynomials, preprint (2017) arXiv:1707.06207
33	M Tange, The E₈–boundings of homology spheres and negative sphere classes in E(1), Topology Appl. 202 (2016) 160 MR3464158
34	M Thaddeus, A perfect Morse function on the moduli space of flat connections, Topology 39 (2000) 773 MR1760428