Volume 17, issue 2 (2013)

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Kervaire invariants and selfcoincidences

Ulrich Koschorke and Duane Randall

Geometry & Topology 17 (2013) 621–638
Bibliography
1 J F Adams, On the non-existence of elements of Hopf invariant one, Ann. of Math. 72 (1960) 20 MR0141119
2 M G Barratt, J D S Jones, M E Mahowald, The Kervaire invariant problem, from: "Proceedings of the Northwestern Homotopy Theory Conference" (editors H R Miller, S B Priddy), Contemp. Math. 19, Amer. Math. Soc. (1983) 9 MR711039
3 M G Barratt, J D S Jones, M E Mahowald, Relations amongst Toda brackets and the Kervaire invariant in dimension $62$, J. London Math. Soc. 30 (1984) 533 MR810962
4 M G Barratt, J D S Jones, M E Mahowald, The Kervaire invariant and the Hopf invariant, from: "Algebraic topology" (editors H R Miller, D C Ravenel), Lecture Notes in Math. 1286, Springer (1987) 135 MR922925
5 J M Boardman, B Steer, On Hopf invariants, Comment. Math. Helv. 42 (1967) 180 MR0221503
6 W Browder, The Kervaire invariant of framed manifolds and its generalization, Ann. of Math. 90 (1969) 157 MR0251736
7 E H Brown Jr., F P Peterson, Whitehead products and cohomology operations, Quart. J. Math. Oxford Ser. 15 (1964) 116 MR0161341
8 R F Brown, Wecken properties for manifolds, from: "Nielsen theory and dynamical systems" (editor C K McCord), Contemp. Math. 152, Amer. Math. Soc. (1993) 9 MR1243467
9 F R Cohen, Fibration and product decompositions in nonstable homotopy theory, from: "Handbook of algebraic topology" (editor I M James), North-Holland (1995) 1175 MR1361909
10 M C Crabb, The homotopy coincidence index, J. Fixed Point Theory Appl. 7 (2010) 1 MR2652509
11 A Dold, D L Gonçalves, Self-coincidence of fibre maps, Osaka J. Math. 42 (2005) 291 MR2147735
12 M Golasiński, J Mukai, Gottlieb groups of spheres, Topology 47 (2008) 399 MR2427733
13 D L Gonçalves, D Randall, Self-coincidence of maps from $S^q$–bundles over $S^n$ to $S^n$, Bol. Soc. Mat. Mexicana 10 (2004) 181 MR2199347
14 D Gonçalves, D Randall, Self-coincidence of mappings between spheres and the strong Kervaire invariant one problem, C. R. Math. Acad. Sci. Paris 342 (2006) 511 MR2214606
15 M Hill, M Hopkins, D Ravenel, On the non-existence of elements of Kervaire invariant one (2010) arXiv:0908.37254v2
16 I M James, Products on spheres, Mathematika 6 (1959) 1 MR0148067
17 M A Kervaire, A manifold which does not admit any differentiable structure, Comment. Math. Helv. 34 (1960) 257 MR0139172
18 M A Kervaire, J W Milnor, Groups of homotopy spheres, I, Ann. of Math. 77 (1963) 504 MR0148075
19 S O Kochman, M E Mahowald, On the computation of stable stems, from: "The Čech centennial" (editors M Cenkl, H Miller), Contemp. Math. 181, Amer. Math. Soc. (1995) 299 MR1320997
20 U Koschorke, Selfcoincidences in higher codimensions, J. Reine Angew. Math. 576 (2004) 1 MR2099198
21 U Koschorke, Nonstabilized Nielsen coincidence invariants and Hopf–Ganea homomorphisms, Geom. Topol. 10 (2006) 619 MR2240900
22 U Koschorke, Minimizing coincidence numbers of maps into projective spaces, from: "The Zieschang Gedenkschrift" (editors M Boileau, M Scharlemann, R Weidmann), Geom. Topol. Monogr. 14, Geom. Topol. Publ., Coventry (2008) 373 MR2484710
23 U Koschorke, Minimum numbers and Wecken theorems in topological coincidence theory, I, J. Fixed Point Theory Appl. 10 (2011) 3 MR2825738
24 K Y Lam, D Randall, Block bundle obstruction to Kervaire invariant one, from: "Recent developments in algebraic topology" (editors A Ádem, J González, G Pastor), Contemp. Math. 407, Amer. Math. Soc. (2006) 163 MR2248977
25 J Milnor, Differential topology forty-six years later, Notices Amer. Math. Soc. 58 (2011) 804 MR2839925
26 Y Nomura, Some homotopy groups of real Stiefel manifolds in the metastable range, V, Sci. Rep. College Gen. Ed. Osaka Univ. 29 (1980) 159 MR626477
27 H Toda, Composition methods in homotopy groups of spheres, Annals of Mathematics Studies 49, Princeton Univ. Press (1962) MR0143217
28 G W Whitehead, Elements of homotopy theory, Graduate Texts in Mathematics 61, Springer (1978) MR516508