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$\mathrm{Pin}(2)$–equivariant KO–theory and intersection forms of spin $4$–manifolds

Jianfeng Lin

Algebraic & Geometric Topology 15 (2015) 863–902
Bibliography
1 J F Adams, Prerequisites (on equivariant stable homotopy) for Carlsson's lecture, from: "Algebraic topology" (editors I Madsen, B Oliver), Lecture Notes in Math. 1051, Springer (1984) 483 MR764596
2 M F Atiyah, $K\!$–theory, W A Benjamin MR0224083
3 M F Atiyah, $K\!$–theory and reality, Quart. J. Math. Oxford Ser. 17 (1966) 367 MR0206940
4 M F Atiyah, Bott periodicity and the index of elliptic operators, Quart. J. Math. Oxford Ser. 19 (1968) 113 MR0228000
5 M F Atiyah, G B Segal, Equivariant $K\!$–theory and completion, J. Differential Geometry 3 (1969) 1 MR0259946
6 T tom Dieck, Transformation groups and representation theory, Lecture Notes in Mathematics 766, Springer (1979) MR551743
7 T tom Dieck, Transformation groups, de Gruyter Studies in Mathematics 8, Walter de Gruyter & Co. (1987) MR889050
8 S K Donaldson, An application of gauge theory to four-dimensional topology, J. Differential Geom. 18 (1983) 279 MR710056
9 S K Donaldson, The orientation of Yang–Mills moduli spaces and $4$–manifold topology, J. Differential Geom. 26 (1987) 397 MR910015
10 K A Frøyshov, The Seiberg–Witten equations and four-manifolds with boundary, Math. Res. Lett. 3 (1996) 373 MR1397685
11 K A Frøyshov, Equivariant aspects of Yang–Mills Floer theory, Topology 41 (2002) 525 MR1910040
12 K A Frøyshov, Monopole Floer homology for rational homology $3$–spheres, Duke Math. J. 155 (2010) 519 MR2738582
13 Y Fukumoto, M Furuta, Homology $3$–spheres bounding acyclic $4$–manifolds, Math. Res. Lett. 7 (2000) 757 MR1809299
14 M Furuta, Monopole equation and the $\frac{11}8$–conjecture, Math. Res. Lett. 8 (2001) 279 MR1839478
15 M Furuta, Y Kametani, Equivariant maps between sphere bundles over tori and $\mathrm{KO}$–degree, arXiv:0502511
16 M Furuta, T J Li, Intersection forms of spin $4$–manifolds with boundary, preprint (2013)
17 P Kronheimer, T Mrowka, P Ozsváth, Z Szabó, Monopoles and lens space surgeries, Ann. of Math. 165 (2007) 457 MR2299739
18 C Manolescu, $\mathrm{Pin}(2)$–equivariant Seiberg–Witten Floer homology and the triangulation conjecture, arXiv:1303.2354v2
19 C Manolescu, Seiberg–Witten–Floer stable homotopy type of three-manifolds with $b_1=0$, Geom. Topol. 7 (2003) 889 MR2026550
20 C Manolescu, A gluing theorem for the relative Bauer–Furuta invariants, J. Differential Geom. 76 (2007) 117 MR2312050
21 C Manolescu, On the intersection forms of spin four-manifolds with boundary, Math. Ann. 359 (2014) 695 MR3231012
22 Y Matsumoto, On the bounding genus of homology $3$–spheres, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 29 (1982) 287 MR672065
23 N Minami, The $G$–join theorem: An unbased $G$–Freudenthal theorem, preprint
24 W D Neumann, An invariant of plumbed homology spheres, from: "Topology Symposium" (editors U Koschorke, W D Neumann), Lecture Notes in Math. 788, Springer (1980) 125 MR585657
25 W D Neumann, F Raymond, Seifert manifolds, plumbing, $\mu $–invariant and orientation reversing maps, from: "Algebraic and geometric topology" (editor K C Millett), Lecture Notes in Math. 664, Springer (1978) 163 MR518415
26 P Ozsváth, Z Szabó, Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary, Adv. Math. 173 (2003) 179 MR1957829
27 V A Rokhlin, New results in the theory of four-dimensional manifolds, Doklady Akad. Nauk SSSR 84 (1952) 221 MR0052101
28 N Saveliev, Fukumoto–Furuta invariants of plumbed homology $3$–spheres, Pacific J. Math. 205 (2002) 465 MR1922741
29 B Schmidt, Spin $4$–manifolds and $\mathrm{Pin}(2)$–equivariant homotopy theory, PhD thesis, Universität Bielefield (2003)
30 G Segal, Equivariant $K\!$–theory, Inst. Hautes Études Sci. Publ. Math. (1968) 129 MR0234452
31 L Siebenmann, On vanishing of the Rokhlin invariant and nonfinitely amphicheiral homology $3$–spheres, from: "Topology Symposium" (editors U Koschorke, W D Neumann), Lecture Notes in Math. 788, Springer (1980) 172 MR585660
32 S Stolz, The level of real projective spaces, Comment. Math. Helv. 64 (1989) 661 MR1023002