Volume 18, issue 1 (2014)

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The pillowcase and perturbations of traceless representations of knot groups

Matthew Hedden, Christopher M Herald and Paul Kirk

Geometry & Topology 18 (2014) 211–287
Bibliography
1 S Akbulut, J D McCarthy, Casson's invariant for oriented homology $3$–spheres, Mathematical Notes 36, Princeton Univ. Press (1990) MR1030042
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 D Bar-Natan, The Mathematica package KnotTheory
4 H U Boden, C M Herald, P A Kirk, E P Klassen, Gauge theoretic invariants of Dehn surgeries on knots, Geom. Topol. 5 (2001) 143 MR1825661
5 G Burde, $\mathrm{SU}(2)$–representation spaces for two-bridge knot groups, Math. Ann. 288 (1990) 103 MR1070927
6 G Burde, H Zieschang, Knots, de Gruyter Studies in Mathematics 5, de Gruyter (1985) MR808776
7 D Cooper, M Culler, H Gillet, D D Long, P B Shalen, Plane curves associated to character varieties of $3$–manifolds, Invent. Math. 118 (1994) 47 MR1288467
8 M Daniel, P A Kirk, A general splitting formula for the spectral flow, Michigan Math. J. 46 (1999) 589 MR1721567
9 A Floer, Instanton homology, surgery, and knots, from: "Geometry of low-dimensional manifolds, $1$" (editors S K Donaldson, C B Thomas), London Math. Soc. Lecture Note Ser. 150, Cambridge Univ. Press (1990) 97 MR1171893
10 Y Fukumoto, P A Kirk, J Pinzón-Caicedo, Traceless $\mathrm{SU}(2)$ representations of $2$–stranded tangles arXiv:1305.6042
11 B Gerard, Singular connections on $3$–manifolds and manifolds with cylindrical ends arXiv:math/9805036
12 C M Herald, Legendrian cobordism and Chern–Simons theory on $3$–manifolds with boundary, Comm. Anal. Geom. 2 (1994) 337 MR1305710
13 C M Herald, Flat connections, the Alexander invariant, and Casson's invariant, Comm. Anal. Geom. 5 (1997) 93 MR1456309
14 M Heusener, J Kroll, Deforming abelian $\mathrm{SU}(2)$–representations of knot groups, Comment. Math. Helv. 73 (1998) 480 MR1633375
15 M Jacobsson, R L Rubinsztein, Symplectic topology of $\mathrm{SU}(2)$–representation varieties and link homology, I: Symplectic braid action and the first Chern class arXiv:0806.2902
16 M Khovanov, A categorification of the Jones polynomial, Duke Math. J. 101 (2000) 359 MR1740682
17 M Khovanov, Patterns in knot cohomology, I, Experiment. Math. 12 (2003) 365 MR2034399
18 P A Kirk, E P Klassen, Chern–Simons invariants of $3$–manifolds and representation spaces of knot groups, Math. Ann. 287 (1990) 343 MR1054574
19 P A Kirk, C Livingston, Concordance and mutation, Geom. Topol. 5 (2001) 831 MR1871406
20 E P Klassen, Representations of knot groups in $\mathrm{SU}(2)$, Trans. Amer. Math. Soc. 326 (1991) 795 MR1008696
21 P B Kronheimer, T S Mrowka, Filtrations on instanton homology arXiv:1110.1290
22 P B Kronheimer, T S Mrowka, Dehn surgery, the fundamental group and $\mathrm{SU}(2)$, Math. Res. Lett. 11 (2004) 741 MR2106239
23 P B Kronheimer, T S Mrowka, Instanton Floer homology and the Alexander polynomial, Algebr. Geom. Topol. 10 (2010) 1715 MR2683750
24 P B Kronheimer, T S Mrowka, Knots, sutures, and excision, J. Differential Geom. 84 (2010) 301 MR2652464
25 P B Kronheimer, T S Mrowka, Khovanov homology is an unknot-detector, Publ. Math. Inst. Hautes Études Sci. (2011) 97 MR2805599
26 P B Kronheimer, T S Mrowka, Knot homology groups from instantons, J. Topol. 4 (2011) 835 MR2860345
27 E S Lee, An endomorphism of the Khovanov invariant, Adv. Math. 197 (2005) 554 MR2173845
28 S Lewallen, Khovanov homology of alternating links and $\mathrm{SU}(2)$ representations of the link group arXiv:0910.5047
29 Y Lim, Instanton homology and the Alexander polynomial, Proc. Amer. Math. Soc. 138 (2010) 3759 MR2661575
30 X S Lin, A knot invariant via representation spaces, J. Differential Geom. 35 (1992) 337 MR1158339
31 C Manolescu, P Ozsváth, On the Khovanov and knot Floer homologies of quasi-alternating links, from: "Proceedings of Gökova Geometry–Topology Conference 2007", GGT (2008) 60 MR2509750
32 L I Nicolaescu, The Maslov index, the spectral flow, and decompositions of manifolds, Duke Math. J. 80 (1995) 485 MR1369400
33 P Ozsváth, Z Szabó, Holomorphic disks and knot invariants, Adv. Math. 186 (2004) 58 MR2065507
34 P Ozsváth, Z Szabó, On knot Floer homology and lens space surgeries, Topology 44 (2005) 1281 MR2168576
35 T R Ramadas, I M Singer, J Weitsman, Some comments on Chern–Simons gauge theory, Comm. Math. Phys. 126 (1989) 409 MR1027504
36 J A Rasmussen, Floer homology and knot complements, PhD Thesis, Harvard University (2003)
37 R Riley, Nonabelian representations of $2$–bridge knot groups, Quart. J. Math. Oxford Ser. 35 (1984) 191 MR745421
38 P Turner, A spectral sequence for Khovanov homology with an application to $(3,q)$–torus links, Algebr. Geom. Topol. 8 (2008) 869 MR2443099
39 K Wehrheim, C T Woodward, Functoriality for Lagrangian correspondences in Floer theory, Quantum Topol. 1 (2010) 129 MR2657646
40 A Weil, Remarks on the cohomology of groups, Ann. of Math. 80 (1964) 149 MR0169956
41 R Zentner, Representation spaces of pretzel knots, Algebr. Geom. Topol. 11 (2011) 2941 MR2869448