#### Volume 16, issue 6 (2016)

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Strong Heegaard diagrams and strong L–spaces

### Joshua Evan Greene and Adam Simon Levine

Algebraic & Geometric Topology 16 (2016) 3167–3208
##### Bibliography
 1 C Bankwitz, Über die Torsionszahlen der alternierenden Knoten, Math. Ann. 103 (1930) 145 MR1512619 2 J Berge, Some knots with surgeries yielding lens spaces, unpublished (1990) 3 S Boyer, C M Gordon, L Watson, On L–spaces and left-orderable fundamental groups, Math. Ann. 356 (2013) 1213 MR3072799 4 G E Bredon, J W Wood, Non-orientable surfaces in orientable 3–manifolds, Invent. Math. 7 (1969) 83 MR0246312 5 A J Casson, C M Gordon, Reducing Heegaard splittings, Topology Appl. 27 (1987) 275 MR918537 6 P R Cromwell, Knots and links, Cambridge University Press (2004) MR2107964 7 R H Crowell, Nonalternating links, Illinois J. Math. 3 (1959) 101 MR0099667 8 N M Dunfield, W P Thurston, The virtual Haken conjecture : experiments and examples, Geom. Topol. 7 (2003) 399 MR1988291 9 C M Gordon, Dehn surgery and 3–manifolds, from: "Low dimensional topology" (editors T S Mrowka, P S Ozsváth), IAS/Park City Math. Ser. 15, Amer. Math. Soc. (2009) 21 MR2503492 10 J E Greene, Lattices, graphs, and Conway mutation, Invent. Math. 192 (2013) 717 MR3049933 11 J E Greene, A spanning tree model for the Heegaard Floer homology of a branched double-cover, J. Topol. 6 (2013) 525 MR3065184 12 J E Greene, L Watson, Turaev torsion, definite 4–manifolds, and quasi-alternating knots, Bull. Lond. Math. Soc. 45 (2013) 962 MR3104988 13 0 m 1 W Haken, Some results on surfaces in 3–manifolds, from: "Studies in Modern Topology" (editor P J Hilton), Math. Assoc. Amer. (1968) 39 MR0224071 14 J Hanselman, J Rasmussen, S D Rasmussen, L Watson, Taut foliations on graph manifolds, preprint (2015) arXiv:1508.0591 15 J Hanselman, L Watson, A calculus for bordered Floer homology, preprint (2015) arXiv:1508.05445 16 M Hedden, On Floer homology and the Berge conjecture on knots admitting lens space surgeries, Trans. Amer. Math. Soc. 363 (2011) 949 MR2728591 17 G Hetyei, 2 × 1-es téglalapokkal lefedhető idomokról (Rectangular configurations which can be covered by 2 × 1 rectangles), Pécsi Tanárk. Főisk. Közl. 8 (1964) 351 18 T Homma, M Ochiai, M o Takahashi, An algorithm for recognizing S3 in 3–manifolds with Heegaard splittings of genus two, Osaka J. Math. 17 (1980) 625 MR591141 19 W H Kazez, R Roberts, Approximating C1,0 foliations, preprint (2014) arXiv:1404.5919 20 D A Lee, R Lipshitz, Covering spaces and ℚ–gradings on Heegaard Floer homology, J. Symplectic Geom. 6 (2008) 33 MR2417439 21 A S Levine, S Lewallen, Strong L–spaces and left-orderability, Math. Res. Lett. 19 (2012) 1237 MR3091604 22 A S Levine, D Ruberman, S Strle, Nonorientable surfaces in homology cobordisms, Geom. Topol. 19 (2015) 439 MR3318756 23 L Lovász, M D Plummer, Matching theory, AMS Chelsea Publishing (2009) MR2536865 24 B Martelli, C Petronio, F Roukema, Exceptional Dehn surgery on the minimally twisted five-chain link, Comm. Anal. Geom. 22 (2014) 689 MR3263935 25 W McCuaig, Pólya’s permanent problem, Electron. J. Combin. 11 (2004) MR2114183 26 W W Menasco, M B Thistlethwaite, The Tait flyping conjecture, Bull. Amer. Math. Soc. 25 (1991) 403 MR1098346 27 O Morikawa, A counterexample to a conjecture of Whitehead, Math. Sem. Notes Kobe Univ. 8 (1980) 295 MR601897 28 Y Ni, Z Wu, Heegaard Floer correction terms and rational genus bounds, Adv. Math. 267 (2014) 360 MR3269182 29 M Ochiai, A counterexample to a conjecture of Whitehead and Volodin–Kuznetsov–Fomenko, J. Math. Soc. Japan 31 (1979) 687 MR544686 30 P Ozsváth, Z Szabó, Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary, Adv. Math. 173 (2003) 179 MR1957829 31 P Ozsváth, Z Szabó, Holomorphic disks and genus bounds, Geom. Topol. 8 (2004) 311 MR2023281 32 P Ozsváth, Z Szabó, Holomorphic disks and knot invariants, Adv. Math. 186 (2004) 58 MR2065507 33 P Ozsváth, Z Szabó, Holomorphic disks and three-manifold invariants: properties and applications, Ann. of Math. 159 (2004) 1159 MR2113020 34 P Ozsváth, Z Szabó, Holomorphic disks and topological invariants for closed three-manifolds, Ann. of Math. 159 (2004) 1027 MR2113019 35 P Ozsváth, Z Szabó, On knot Floer homology and lens space surgeries, Topology 44 (2005) 1281 MR2168576 36 P Ozsváth, Z Szabó, On the Heegaard Floer homology of branched double-covers, Adv. Math. 194 (2005) 1 MR2141852 37 P Ozsváth, Z Szabó, Holomorphic triangles and invariants for smooth four-manifolds, Adv. Math. 202 (2006) 326 MR2222356 38 J A Rasmussen, Floer homology and knot complements, PhD thesis, Harvard University (2003) MR2704683 39 J Rasmussen, Lens space surgeries and L–space homology spheres, preprint (2007) arXiv:0710.2531 40 J Rasmussen, S D Rasmussen, Floer simple manifolds and L–space intervals, preprint (2015) arXiv:1508.05900 41 N Robertson, P D Seymour, R Thomas, Permanents, Pfaffian orientations, and even directed circuits, Ann. of Math. 150 (1999) 929 MR1740989 42 A Schrijver, Tait’s flyping conjecture for well-connected links, J. Combin. Theory Ser. B 58 (1993) 65 MR1214893 43 T Usui, Heegaard Floer homology, L–spaces, and smoothing order on links, I, preprint (2012) arXiv:1202.1353 44 T Usui, Heegaard Floer homology, L–spaces, and smoothing order on links, II, preprint (2012) arXiv:1202.3333 45 V V Vazirani, M Yannakakis, Pfaffian orientations, 0–1 permanents, and even cycles in directed graphs, Discrete Appl. Math. 25 (1989) 179 MR1031270 46 O J Viro, V L Kobel’skiĭ, The Volodin–Kuznecov–Fomenko conjecture on Heegaard diagrams is false, Uspekhi Mat. Nauk 32 (1977) 175 MR0467757 47 I A Volodin, V E Kuznetsov, A T Fomenko, The problem of discriminating algorithmically the standard three-dimensional sphere, Uspekhi Mat. Nauk 29 (1974) 71 MR405426 48 M Voorhoeve, A lower bound for the permanents of certain (0,1)–matrices, Nederl. Akad. Wetensch. Indag. Math. 41 (1979) 83 MR528221