Geometry & Topology Volume 18, issue 4 (2014)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author Index

To Appear

Other MSP Journals

The Cayley plane and string bordism

Carl McTague

Geometry & Topology 18 (2014) 2045–2078

DOI: 10.2140/gt.2014.18.2045

Bibliography

1	D W Anderson, E H Brown Jr., F P Peterson, The structure of the Spin cobordism ring, Ann. of Math. 86 (1967) 271 MR0219077
2	A Borel, J De Siebenthal, Les sous-groupes fermés de rang maximum des groupes de Lie clos, Comment. Math. Helv. 23 (1949) 200 MR0032659
3	A Borel, F Hirzebruch, Characteristic classes and homogeneous spaces, I, Amer. J. Math. 80 (1958) 458 MR0102800
4	A Borel, F Hirzebruch, Characteristic classes and homogeneous spaces, II, Amer. J. Math. 81 (1959) 315 MR0110105
5	N Bourbaki, Éléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: Systèmes de racines, Actualités Scientifiques et Industrielles 1337, Hermann, Paris (1968) MR0240238
6	E H Brown Jr., F P Peterson, A spectrum whose $Z_{p}$ cohomology is the algebra of reduced $p^\mathit{th}$ powers, Topology 5 (1966) 149 MR0192494
7	A Dessai, The Witten genus and $\mathrm{S}^3$–actions on manifolds, Preprint No. 6 (1994) MR2581907
8	A Dessai, Rigidity theorems for $\mathrm{Spin}^{\mathrm{c}}$–manifolds and applications, PhD thesis, Universität Mainz (1996)
9	A Dessai, Some geometric properties of the Witten genus, from: "Alpine perspectives on algebraic topology" (editors C Ausoni, K Hess, J Scherer), Contemp. Math. 504, Amer. Math. Soc. (2009) 99 MR2581907
10	A Dold, Erzeugende der Thomschen Algebra $\mathfrak{N}$, Math. Zeit. 65 (1956) 25 MR0079269
11	S Führing, Bordismus und $\mathbf{C}\mathrm{P}^2$–Bündel, diploma thesis, Universität München (2008)
12	V Giambalvo, On $\langle 8\rangle$–cobordism, Illinois J. Math. 15 (1971) 533 MR0287553
13	A Granville, Arithmetic properties of binomial coefficients, I: Binomial coefficients modulo prime powers, from: "Organic mathematics" (editors J Borwein, P Borwein, L Jörgenson, R Corless), CMS Conf. Proc. 20, Amer. Math. Soc. (1997) 253 MR1483922
14	G H Hardy, E M Wright, An introduction to the theory of numbers, Clarendon Press (1979) MR568909
15	M A Hovey, The homotopy of $M \mathrm String$ and $M \mathrm U\langle 6\rangle$ at large primes, Algebr. Geom. Topol. 8 (2008) 2401 MR2465746
16	M A Hovey, D C Ravenel, The $7$–connected cobordism ring at $p=3$, Trans. Amer. Math. Soc. 347 (1995) 3473 MR1297530
17	D C Johnson, W S Wilson, Projective dimension and Brown–Peterson homology, Topology 12 (1973) 327 MR0334257
18	M Kreck, S Stolz, $\mathbf{H}\mathrm{P}^2$–bundles and elliptic homology, Acta Math. 171 (1993) 231 MR1251581
19	K Liu, On elliptic genera and Jacobi forms, (1992)
20	C McTague, $\mathrm{tmf}$ is not a ring spectrum quotient of String bordism, arXiv:1312.2440
21	J W Milnor, On the Stiefel–Whitney numbers of complex manifolds and of spin manifolds, Topology 3 (1965) 223 MR0180977
22	J W Milnor, J D Stasheff, Characteristic classes, Annals of Mathematics Studies 76, Princeton Univ. Press (1974) MR0440554
23	F Morley, Note on the congruence $2^{4n}\equiv(-)^n(2n)!/(n!)^2$, where $2n+1$ is a prime, Ann. of Math. 9 (1894/95) 168 MR1502188
24	D C Ravenel, Complex cobordism and stable homotopy groups of spheres, Pure and Applied Mathematics 121, Academic Press (1986) MR860042
25	D C Ravenel, W S Wilson, The Hopf ring for complex cobordism, Bull. Amer. Math. Soc. 80 (1974) 1185 MR0356030
26	S Stolz, Splitting certain $M \mathrm{Spin}$–module spectra, Topology 33 (1994) 159 MR1259520
27	S Stolz, A conjecture concerning positive Ricci curvature and the Witten genus, Math. Ann. 304 (1996) 785 MR1380455
28	R E Stong, Notes on cobordism theory, Mathematical notes, Princeton Univ. Press (1968) MR0248858
29	R E Stong, On fibering of cobordism classes, Trans. Amer. Math. Soc. 178 (1973) 431 MR0315733
30	R Thom, Quelques propriétés globales des variétés différentiables, Comment. Math. Helv. 28 (1954) 17 MR0061823
31	C T C Wall, Determination of the cobordism ring, Ann. of Math. 72 (1960) 292 MR0120654
32	W S Wilson, The $\Omega $–spectrum for Brown–Peterson cohomology, II, Amer. J. Math. 97 (1975) 101 MR0383390