Volume 17, issue 2 (2013)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 29
Issue 5, 2251–2782
Issue 4, 1693–2250
Issue 3, 1115–1691
Issue 2, 549–1114
Issue 1, 1–548

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
 
Author index
To appear
 
Other MSP journals
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