Geometry & Topology Volume 29, issue 4 (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

Relations in singular instanton homology

Peter B Kronheimer and Tomasz S Mrowka

Geometry & Topology 29 (2025) 1975–2046

DOI: 10.2140/gt.2025.29.1975

Bibliography

1	M F Atiyah, R Bott, The Yang–Mills equations over Riemann surfaces, Philos. Trans. Roy. Soc. A 308 (1983) 523 MR0702806
2	I Biswas, N Raghavendra, Canonical generators of the cohomology of moduli of parabolic bundles on curves, Math. Ann. 306 (1996) 1 MR1405316
3	H U Boden, Representations of orbifold groups and parabolic bundles, PhD thesis, Brandeis University (1991)
4	C Casagrande, Rank 2 quasiparabolic vector bundles on ℙ¹ and the variety of linear subspaces contained in two odd-dimensional quadrics, Math. Z. 280 (2015) 981 MR3369361
5	A Daemi, C Scaduto, Equivariant aspects of singular instanton Floer homology, preprint (2019) arXiv:1912.08982
6	S K Donaldson, The orientation of Yang–Mills moduli spaces and 4-manifold topology, J. Differential Geom. 26 (1987) 397 MR0910015
7	S Dostoglou, D A Salamon, Self-dual instantons and holomorphic curves, Ann. of Math. 139 (1994) 581 MR1283871
8	R Earl, F Kirwan, Complete sets of relations in the cohomology rings of moduli spaces of holomorphic bundles and parabolic bundles over a Riemann surface, Proc. Lond. Math. Soc. 89 (2004) 570 MR2107008
9	D Eisenbud, The geometry of syzygies: a second course in commutative algebra and algebraic geometry, 229, Springer (2005) MR2103875
10	R Fintushel, R J Stern, Instanton homology of Seifert fibred homology three spheres, Proc. Lond. Math. Soc. 61 (1990) 109 MR1051101
11	W M Goldman, The symplectic nature of fundamental groups of surfaces, Adv. Math. 54 (1984) 200 MR0762512
12	Y H Kiem, On the redundancy of the Mumford relations, J. Algebraic Geom. 9 (2000) 395 MR1735778
13	P A Kirk, E P Klassen, Representation spaces of Seifert fibered homology spheres, Topology 30 (1991) 77 MR1081935
14	F Kirwan, The cohomology rings of moduli spaces of bundles over Riemann surfaces, J. Amer. Math. Soc. 5 (1992) 853 MR1145826
15	U Koschorke, Infinite-dimensional K-theory and characteristic classes of Fredholm bundle maps, from: "Global analysis" (editors S s Chern, S Smale), Proc. Sympos. Pure Math. 15, Amer. Math. Soc. (1970) 95 MR0279838
16	P B Kronheimer, An obstruction to removing intersection points in immersed surfaces, Topology 36 (1997) 931 MR1432428
17	P B Kronheimer, T S Mrowka, Gauge theory for embedded surfaces, I, Topology 32 (1993) 773 MR1241873
18	P B Kronheimer, T S Mrowka, Gauge theory for embedded surfaces, II, Topology 34 (1995) 37 MR1308489
19	P B Kronheimer, T S Mrowka, Khovanov homology is an unknot-detector, Publ. Math. Inst. Hautes Études Sci. 113 (2011) 97 MR2805599
20	P B Kronheimer, T S Mrowka, Knot homology groups from instantons, J. Topol. 4 (2011) 835 MR2860345
21	P B Kronheimer, T S Mrowka, A deformation of instanton homology for webs, Geom. Topol. 23 (2019) 1491 MR3956896
22	P B Kronheimer, T S Mrowka, Tait colorings, and an instanton homology for webs and foams, J. Eur. Math. Soc. 21 (2019) 55 MR3880205
23	P B Kronheimer, T S Mrowka, Instantons and Bar-Natan homology, Compos. Math. 157 (2021) 484 MR4236193
24	P B Kronheimer, T S Mrowka, Instantons and some concordance invariants of knots, J. Lond. Math. Soc. 104 (2021) 541 MR4311103
25	V B Mehta, C S Seshadri, Moduli of vector bundles on curves with parabolic structures, Math. Ann. 248 (1980) 205 MR0575939
26	E Miller, B Sturmfels, Combinatorial commutative algebra, 227, Springer (2005) MR2110098
27	V Muñoz, Quantum cohomology of the moduli space of stable bundles over a Riemann surface, Duke Math. J. 98 (1999) 525 MR1695800
28	V Muñoz, Ring structure of the Floer cohomology of Σ × 𝕊¹, Topology 38 (1999) 517 MR1670396
29	I R Porteous, Simple singularities of maps, from: "Proceedings of Liverpool Singularities : symposium I" (editor C T C Wall), Lecture Notes in Math. 192, Springer (1971) 286 MR0293646
30	P Seidel, A long exact sequence for symplectic Floer cohomology, Topology 42 (2003) 1003 MR1978046
31	P Seidel, Lectures on four-dimensional Dehn twists, from: "Symplectic 4-manifolds and algebraic surfaces" (editors F Catanese, G Tian), Lecture Notes in Math. 1938, Springer (2008) 231 MR2441414
32	E J Street, Towards an instanton Floer homology for tangles, PhD thesis, Harvard University (2012) MR3054928
33	M Thaddeus, Conformal field theory and the cohomology of the moduli space of stable bundles, J. Differential Geom. 35 (1992) 131 MR1152228
34	K Wehrheim, C T Woodward, Exact triangle for fibered Dehn twists, Res. Math. Sci. 3 (2016) 17 MR3536436
35	J Weitsman, Geometry of the intersection ring of the moduli space of flat connections and the conjectures of Newstead and Witten, Topology 37 (1998) 115 MR1480881
36	Y Xie, B Zhang, Instanton Floer homology for sutured manifolds with tangles, preprint (2019) arXiv:1907.00547
37	D Zagier, On the cohomology of moduli spaces of rank two vector bundles over curves, from: "The moduli space of curves" (editors R Dijkgraaf, C Faber, G van der Geer), Progr. Math. 129, Birkhäuser (1995) 533 MR1363070