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This paper shows that, away from 6, the kernel of the Witten genus is precisely the ideal consisting of (bordism classes of) Cayley plane bundles with connected structure group, but only after restricting the Witten genus to string bordism.
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A. Borel and J. De Siebenthal · 1949
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Quelques propriétés globales des variétés différentiables
René Thom · 1954
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Erzeugende der Thomschen Algebra 𝔑 {\mathfrak{N}}
Albrecht Dold · 1956
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Characteristic classes and homogeneous spaces. I
A. Borel and F. Hirzebruch · 1958
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Characteristic classes and homogeneous spaces. II
A. Borel and F. Hirzebruch · 1959
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Determination of the cobordism ring
C. T. C. Wall · 1960
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On the Stiefel-Whitney numbers of complex manifolds and of spin manifolds
J. Milnor · 1965
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A spectrum whose Z p Z_{p} cohomology is the algebra of reduced p t h p^{th} powers
Edgar H. Brown, Jr. and Franklin P. Peterson · 1966
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The structure of the Spin cobordism ring
D. W. Anderson, E. H. Brown, Jr., and F. P. Peterson · 1967
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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
N. Bourbaki · 1968
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Notes on cobordism theory
Robert E. Stong · 1968
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On ⟨ 8 ⟩ \langle 8\rangle -cobordism
V. Giambalvo · 1971
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Projective dimension and Brown-Peterson homology
David Copeland Johnson and W. Stephen Wilson · 1973
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On fibering of cobordism classes
R. E. Stong · 1973
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Characteristic classes
John W. Milnor and James D. Stasheff · 1974
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The Hopf ring for complex cobordism
Douglas C. Ravenel and W. Stephen Wilson · 1974
Cited alongside, same era.
The Ω \Omega -spectrum for Brown-Peterson cohomology. II
W. Stephen Wilson · 1975
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An introduction to the theory of numbers
G. H. Hardy and E. M. Wright · 1979
The Witten genus and S 3 \mathrm{S}^{3} -actions on manifolds
Anand Dessai · 1994
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Splitting certain M Spin M\,{\rm Spin} -module spectra
Stephan Stolz · 1994
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The 7 7 -connected cobordism ring at p = 3 p=3
Mark A. Hovey and Douglas C. Ravenel · 1995
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Rigidity theorems for Spin c -manifolds and applications
Anand Dessai · 1996
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A conjecture concerning positive Ricci curvature and the Witten genus
Stephan Stolz · 1996
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Arithmetic properties of binomial coefficients. I. Binomial coefficients modulo prime powers
Andrew Granville · 1997
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Complex cobordism and stable homotopy groups of spheres
Douglas C. Ravenel · 1986
Cited alongside, same era.
On elliptic genera and Jacobi forms
Kefeng Liu · 1992
Cited alongside, same era.
𝐇 P 2 {\bf H}{\rm P}^{2} -bundles and elliptic homology
Matthias Kreck and Stephan Stolz · 1993
Cited alongside, same era.
Note on the congruence 2 4 n ≡ ( − ) n ( 2 n ) ! / ( n ! ) 2 2^{4n}\equiv(-)^{n}(2n)!/(n!)^{2} , where 2 n + 1 2n+1 is a prime
F. Morley
Cited in the paper.
Bordismus und 𝐂 P 2 \mathbf{C}\mathrm{P}^{2} -Bündel
Sven Führing · 2008
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The homotopy of M String M\,\rm String and M U ⟨ 6 ⟩ M\,\rm U\langle 6\rangle at large primes
Mark Hovey · 2008
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Some geometric properties of the Witten genus
Anand Dessai · 2009
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tmf is not a ring spectrum quotient of String bordism
Carl McTague · 2013
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