Geometry & Topology Volume 21, issue 4 (2017)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

The simplicial suspension sequence in $\mathbb{A}^1\mskip-2mu$–homotopy

Aravind Asok, Kirsten Wickelgren and Ben Williams

Geometry & Topology 21 (2017) 2093–2160

DOI: 10.2140/gt.2017.21.2093

Bibliography

1	M Arkowitz, The generalized Whitehead product, Pacific J. Math. 12 (1962) 7 MR0155328
2	A Asok, J Fasel, Toward a meta-stable range in 𝔸1–homotopy theory of punctured affine spaces, Oberwolfach Rep. 10 (2013) 1892 MR3013936
3	A Asok, J Fasel, Algebraic vector bundles on spheres, J. Topol. 7 (2014) 894 MR3252968
4	A Asok, J Fasel, A cohomological classification of vector bundles on smooth affine threefolds, Duke Math. J. 163 (2014) 2561 MR3273577
5	A Asok, J Fasel, Splitting vector bundles outside the stable range and 𝔸1–homotopy sheaves of punctured affine spaces, J. Amer. Math. Soc. 28 (2015) 1031 MR3369908
6	A Asok, J Fasel, Comparing Euler Classes, The Quarterly Journal of Mathematics 67 (2016) 603
7	A Asok, J Fasel, An explicit KO–degree map and applications, Journal of Topology 10 (2017) 268
8	J Ayoub, Un contre-exemple à la conjecture de 𝔸1–connexité de F Morel, C. R. Math. Acad. Sci. Paris 342 (2006) 943 MR2235615
9	W D Barcus, The stable suspension of an Eilenberg–MacLane space, Trans. Amer. Math. Soc. 96 (1960) 101 MR0116330
10	C Barwick, On left and right model categories and left and right Bousfield localizations, Homology Homotopy Appl. 12 (2010) 245 MR2771591
11	H Bass, J Tate, The Milnor ring of a global field, from: "Algebraic K–theory, II : ‘Classical’ algebraic K–theory and connections with arithmetic" (editor H Bass), Springer (1973) MR0442061
12	J M Boardman, B Steer, On Hopf invariants, Comment. Math. Helv. 42 (1967) 180 MR0221503
13	D E Cohen, Products and carrier theory, Proc. London Math. Soc. 7 (1957) 219 MR0087941
14	E B Curtis, Simplicial homotopy theory, Advances in Math. 6 (1971) 107 MR0279808
15	P Deligne, Voevodsky’s lectures on motivic cohomology 2000/2001, from: "Algebraic topology" (editors N A Baas, E M Friedlander, B Jahren, P A Østvær), Abel Symp. 4, Springer (2009) 355 MR2597743
16	D Dugger, D C Isaksen, Topological hypercovers and 𝔸1–realizations, Math. Z. 246 (2004) 667 MR2045835
17	D Dugger, D C Isaksen, Motivic Hopf elements and relations, New York J. Math. 19 (2013) 823 MR3141814
18	R Elman, N Karpenko, A Merkurjev, The algebraic and geometric theory of quadratic forms, 56, Amer. Math. Soc. (2008) MR2427530
19	E D Farjoun, Cellular spaces, null spaces and homotopy localization, 1622, Springer (1996) MR1392221
20	T Ganea, On the homotopy suspension, Comment. Math. Helv. 43 (1968) 225 MR0229239
21	T Geisser, M Levine, The K–theory of fields in characteristic p, Invent. Math. 139 (2000) 459 MR1738056
22	S Gille, S Scully, C Zhong, Milnor–Witt K–groups of local rings, Advances in Mathematics 286 (2016) 729
23	P G Goerss, J F Jardine, Simplicial homotopy theory, 174, Birkhäuser (1999) MR1711612
24	P J Hilton, On the homotopy groups of unions of spaces, Comment. Math. Helv. 29 (1955) 59 MR0069492
25	P S Hirschhorn, Model categories and their localizations, 99, Amer. Math. Soc. (2003) MR1944041
26	A Hogadi, G Kulkarni, Gabber’s presentation lemma for finite fields, preprint (2016) arXiv:1612.09393
27	M Hovey, Model categories, 63, Amer. Math. Soc. (1999) MR1650134
28	D C Isaksen, Etale realization on the 𝔸1–homotopy theory of schemes, Adv. Math. 184 (2004) 37 MR2047848
29	I M James, Reduced product spaces, Ann. of Math. 62 (1955) 170 MR0073181
30	I M James, On the suspension triad, Ann. of Math. 63 (1956) 191 MR0077922
31	I M James, On the suspension sequence, Ann. of Math. 65 (1957) 74 MR0083124
32	J F Jardine, Simplicial presheaves, J. Pure Appl. Algebra 47 (1987) 35 MR906403
33	J F Jardine, Motivic symmetric spectra, Doc. Math. 5 (2000) 445 MR1787949
34	J F Jardine, Local homotopy theory, Springer (2015) MR3309296
35	K Kato, Symmetric bilinear forms, quadratic forms and Milnor K–theory in characteristic two, Invent. Math. 66 (1982) 493 MR662605
36	N J Kuhn, The transfer and James–Hopf invariants, Math. Z. 196 (1987) 391 MR913664
37	J P May, Classifying spaces and fibrations, 155, Amer. Math. Soc. (1975) MR0370579
38	C Mazza, V Voevodsky, C Weibel, Lecture notes on motivic cohomology, 2, Amer. Math. Soc. (2006) MR2242284
39	J Milnor, On the construction FK, from: "Algebraic topology—a student’s guide" (editor J F Adams), London Mathematical Society Lecture Note Series 4, Cambridge University Press (1972) 119 MR0445484
40	F Morel, An introduction to 𝔸1–homotopy theory, from: "Contemporary developments in algebraic K–theory" (editors M Karoubi, A O Kuku, C Pedrini), ICTP Lect. Notes XV, Abdus Salam Int. Cent. Theoret. Phys. (2004) 357 MR2175638
41	F Morel, Sur les puissances de l’idéal fondamental de l’anneau de Witt, Comment. Math. Helv. 79 (2004) 689 MR2099118
42	F Morel, Milnor’s conjecture on quadratic forms and mod 2 motivic complexes, Rend. Sem. Mat. Univ. Padova 114 (2005) 63 MR2207862
43	F Morel, The stable 𝔸1–connectivity theorems, K-Theory 35 (2005) 1 MR2240215
44	F Morel, 𝔸1–algebraic topology over a field, 2052, Springer (2012) MR2934577
45	F Morel, V Voevodsky, A1–homotopy theory of schemes, Inst. Hautes Études Sci. Publ. Math. 90 (1999) 45 MR1813224
46	D Orlov, A Vishik, V Voevodsky, An exact sequence for K∗M∕2 with applications to quadratic forms, Ann. of Math. 165 (2007) 1 MR2276765
47	K M Ormsby, P A Østvær, Stable motivic π1 of low-dimensional fields, Adv. Math. 265 (2014) 97 MR3255457
48	D G Quillen, Homotopical algebra, 43, Springer (1967) MR0223432
49	O Röndigs, M Spitzweck, P A Østvær, The first stable homotopy groups of motivic spheres, preprint (2016) arXiv:1604.00365
50	J P Serre, Cohomologie modulo 2 des complexes d’Eilenberg–MacLane, Comment. Math. Helv. 27 (1953) 198 MR0060234
51	F Strunk, On motivic spherical bundles, PhD thesis, Institut für Mathematik, Universität Osnabrück (2012)
52	H Toda, Composition methods in homotopy groups of spheres, 49, Princeton University Press (1962) MR0143217
53	V Voevodsky, Reduced power operations in motivic cohomology, Publ. Math. Inst. Hautes Études Sci. 98 (2003) 1 MR2031198
54	V Voevodsky, Motivic cohomology with Z∕2–coefficients, Publ. Math. Inst. Hautes Études Sci. 98 (2003) 59 MR2031199
55	V Voevodsky, On motivic cohomology with Z∕l–coefficients, Ann. of Math. 174 (2011) 401 MR2811603
56	M Wendt, Classifying spaces and fibrations of simplicial sheaves, J. Homotopy Relat. Struct. 6 (2011) 1 MR2818697
57	G W Whitehead, A generalization of the Hopf invariant, Ann. of Math. 51 (1950) 192 MR0041435
58	G W Whitehead, On the Freudenthal theorems, Ann. of Math. 57 (1953) 209 MR0055683
59	G W Whitehead, Elements of homotopy theory, 61, Springer (1978) MR516508
60	J H C Whitehead, On adding relations to homotopy groups, Ann. of Math. 42 (1941) 409 MR0004123
61	K Wickelgren, B Williams, The simplicial EHP Sequence in 𝔸1–algebraic topology, preprint (2014) arXiv:1411.5306
62	J Wu, Simplicial objects and homotopy groups, from: "Braids" (editors A J Berrick, F R Cohen, E Hanbury, Y L Wong, J Wu), Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap. 19, World Sci. Publ. (2010) 31 MR2605306