#### Volume 22, issue 5 (2018)

 Download this article For screen For printing
 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Editorial Procedure Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1364-0380 ISSN (print): 1465-3060 Author Index To Appear Other MSP Journals
A splitting theorem for the Seiberg-Witten invariant of a homology $S^1 \times S^3$

### Jianfeng Lin, Daniel Ruberman and Nikolai Saveliev

Geometry & Topology 22 (2018) 2865–2942
##### Bibliography
 1 B Ammann, M Dahl, E Humbert, Surgery and harmonic spinors, Adv. Math. 220 (2009) 523 MR2466425 2 M F Atiyah, V K Patodi, I M Singer, Spectral asymmetry and Riemannian geometry, I, Math. Proc. Cambridge Philos. Soc. 77 (1975) 43 MR0397797 3 J. Baldwin, J. Bloom, The monopole category and invariants of bordered 3–manifolds, in preparation 4 J M Bloom, A link surgery spectral sequence in monopole Floer homology, Adv. Math. 226 (2011) 3216 MR2764887 5 J Bloom, T Mrowka, P Ozsváth, Connected sums in monopole Floer homology, in preparation 6 V Colin, P Ghiggini, K Honda, The equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions, I, preprint (2012) arXiv:1208.1074 7 V Colin, P Ghiggini, K Honda, The equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions, II, preprint (2012) arXiv:1208.1077 8 V Colin, P Ghiggini, K Honda, The equivalence of Heegaard Floer homology and embedded contact homology, III: From hat to plus, preprint (2012) arXiv:1208.1526 9 D Cristofaro-Gardiner, The absolute gradings on embedded contact homology and Seiberg–Witten Floer cohomology, Algebr. Geom. Topol. 13 (2013) 2239 MR3073915 10 R G Douglas, K P Wojciechowski, Adiabatic limits of the η–invariants : the odd-dimensional Atiyah–Patodi–Singer problem, Comm. Math. Phys. 142 (1991) 139 MR1137777 11 K A Frøyshov, Compactness and gluing theory for monopoles, 15, Geometry & Topology Publications (2008) MR2465077 12 K A Frøyshov, Monopole Floer homology for rational homology 3–spheres, Duke Math. J. 155 (2010) 519 MR2738582 13 Y Fukumoto, M Furuta, M Ue, W–invariants and Neumann–Siebenmann invariants for Seifert homology 3–spheres, Topology Appl. 116 (2001) 333 MR1857670 14 M Furuta, H Ohta, Differentiable structures on punctured 4–manifolds, Topology Appl. 51 (1993) 291 MR1237394 15 P B Gilkey, Invariance theory, the heat equation, and the Atiyah–Singer index theorem, 11, Publish or Perish (1984) MR783634 16 F González-Acuña, Dehn’s construction on knots, Bol. Soc. Mat Mexicana 15 (1970) 58 MR0356022 17 K Hendricks, C Manolescu, Involutive Heegaard Floer homology, Duke Math. J. 166 (2017) 1211 MR3649355 18 K Hendricks, C Manolescu, I Zemke, A connected sum formula for involutive Heegaard Floer homology, Selecta Math. 24 (2018) 1183 MR3782421 19 J Hom, Ç Karakurt, T Lidman, Surgery obstructions and Heegaard Floer homology, Geom. Topol. 20 (2016) 2219 MR3548466 20 Y Huang, V G B Ramos, An absolute grading on Heegaard Floer homology by homotopy classes of oriented 2–plane fields, J. Symplectic Geom. 15 (2017) 51 MR3652073 21 M Khovanov, A categorification of the Jones polynomial, Duke Math. J. 101 (2000) 359 MR1740682 22 M Khovanov, Patterns in knot cohomology, I, Experiment. Math. 12 (2003) 365 MR2034399 23 P Kronheimer, T Mrowka, Monopoles and three-manifolds, 10, Cambridge Univ. Press (2007) MR2388043 24 P Kronheimer, T Mrowka, P Ozsváth, Z Szabó, Monopoles and lens space surgeries, Ann. of Math. 165 (2007) 457 MR2299739 25 C Kutluhan, Y J Lee, C H Taubes, HF = HM, I : Heegaard Floer homology and Seiberg–Witten Floer homology, preprint (2010) arXiv:1007.1979 26 C Kutluhan, Y J Lee, C H Taubes, HF = HM, II : Reeb orbits and holomorphic curves for the ech/Heegaard–Floer correspondence, preprint (2010) arXiv:1008.1595 27 C Kutluhan, Y J Lee, C H Taubes, HF = HM, III : Holomorphic curves and the differential for the ech/Heegaard Floer correspondence, preprint (2010) arXiv:1010.3456 28 C Kutluhan, Y J Lee, C H Taubes, HF = HM, IV : The Seiberg–Witten Floer homology and ech correspondence, preprint (2011) arXiv:1107.2297 29 C Kutluhan, Y J Lee, C H Taubes, HF = HM, V : Seiberg–Witten–Floer homology and handle addition, preprint (2012) arXiv:1204.0115 30 A S Levine, D Ruberman, Heegaard Floer invariants in codimension one, preprint (2016) arXiv:1610.03353 31 A Lichnerowicz, Spineurs harmoniques, C. R. Acad. Sci. Paris 257 (1963) 7 MR0156292 32 F Lin, A Morse–Bott approach to monopole Floer homology and the triangulation conjecture, preprint (2014) arXiv:1404.4561 33 J Lin, The Seiberg–Witten equations on end-periodic manifolds and positive scalar curvature metrics, preprint (2016) arXiv:1603.03698 34 J Lin, D Ruberman, N Saveliev, On the Frøyshov invariant and monopole Lefschetz number, preprint (2018) arXiv:1802.07704 35 S Maier, Generic metrics and connections on Spin- and Spinc–manifolds, Comm. Math. Phys. 188 (1997) 407 MR1471821 36 C Manolescu, A gluing theorem for the relative Bauer–Furuta invariants, J. Differential Geom. 76 (2007) 117 MR2312050 37 C Manolescu, An introduction to knot Floer homology, from: "Physics and mathematics of link homology" (editors M Khovanov, J Walcher), Contemp. Math. 680, Amer. Math. Soc. (2016) 99 MR3591644 38 C Manolescu, Pin(2)–equivariant Seiberg–Witten Floer homology and the triangulation conjecture, J. Amer. Math. Soc. 29 (2016) 147 MR3402697 39 C Manolescu, P Ozsváth, On the Khovanov and knot Floer homologies of quasi-alternating links, from: "Proceedings of Gökova Geometry–Topology Conference 2007" (editors S Akbulut, T Önder, R J Stern), GGT (2008) 60 MR2509750 40 T Mrowka, P Ozsváth, B Yu, Seiberg–Witten monopoles on Seifert fibered spaces, Comm. Anal. Geom. 5 (1997) 685 MR1611061 41 T Mrowka, D Ruberman, N Saveliev, Seiberg–Witten equations, end-periodic Dirac operators, and a lift of Rohlin’s invariant, J. Differential Geom. 88 (2011) 333 MR2838269 42 T Mrowka, D Ruberman, N Saveliev, An index theorem for end-periodic operators, Compos. Math. 152 (2016) 399 MR3462557 43 A Némethi, On the Ozsváth–Szabó invariant of negative definite plumbed 3–manifolds, Geom. Topol. 9 (2005) 991 MR2140997 44 Y Ni, Z Wu, Cosmetic surgeries on knots in S3, J. Reine Angew. Math. 706 (2015) 1 MR3393360 45 P Ozsváth, Z Szabó, Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary, Adv. Math. 173 (2003) 179 MR1957829 46 P Ozsváth, Z Szabó, Heegaard Floer homology and alternating knots, Geom. Topol. 7 (2003) 225 MR1988285 47 P Ozsváth, Z Szabó, Holomorphic disks and knot invariants, Adv. Math. 186 (2004) 58 MR2065507 48 P Ozsváth, Z Szabó, Holomorphic disks and three-manifold invariants: properties and applications, Ann. of Math. 159 (2004) 1159 MR2113020 49 P Ozsváth, Z Szabó, On the Heegaard Floer homology of branched double-covers, Adv. Math. 194 (2005) 1 MR2141852 50 P S Ozsváth, Z Szabó, Knot Floer homology and integer surgeries, Algebr. Geom. Topol. 8 (2008) 101 MR2377279 51 P S Ozsváth, Z Szabó, Knot Floer homology and rational surgeries, Algebr. Geom. Topol. 11 (2011) 1 MR2764036 52 V G B Ramos, Absolute gradings on ECH and Heegaard Floer homology, preprint (2014) arXiv:1403.2875 53 J A Rasmussen, Floer homology and knot complements, PhD thesis, Harvard University (2003) MR2704683 54 D Ruberman, N Saveliev, Rohlin’s invariant and gauge theory, II : Mapping tori, Geom. Topol. 8 (2004) 35 MR2033479 55 D Ruberman, N Saveliev, Casson-type invariants in dimension four, from: "Geometry and topology of manifolds" (editors H U Boden, I Hambleton, A J Nicas, B D Park), Fields Inst. Commun. 47, Amer. Math. Soc. (2005) 281 MR2189939 56 D Ruberman, N Saveliev, Dirac operators on manifolds with periodic ends, J. Gökova Geom. Topol. 1 (2007) 33 MR2386534 57 D Ruberman, N Saveliev, The μ–invariant of Seifert fibered homology spheres and the Dirac operator, Geom. Dedicata 154 (2011) 93 MR2832713 58 N Saveliev, Fukumoto–Furuta invariants of plumbed homology 3–spheres, Pacific J. Math. 205 (2002) 465 MR1922741 59 N Saveliev, Invariants for homology 3–spheres, 140, Springer (2002) MR1941324 60 R Schoen, S T Yau, On the structure of manifolds with positive scalar curvature, Manuscripta Math. 28 (1979) 159 MR535700 61 M Stoffregen, Pin(2)–equivariant Seiberg–Witten Floer homology of Seifert fibrations, preprint (2015) arXiv:1505.03234 62 M Stoffregen, Manolescu invariants of connected sums, Proc. Lond. Math. Soc. 115 (2017) 1072 MR3733559 63 C H Taubes, Embedded contact homology and Seiberg–Witten Floer cohomology, I, Geom. Topol. 14 (2010) 2497 MR2746723 64 E Witten, Monopoles and four-manifolds, Math. Res. Lett. 1 (1994) 769 MR1306021