Geodesic
The homotopy of MString and MU〈6〉 at large primes
Hovey, Mark1
1Department of Mathematics and Computer Science, Wesleyan University, Middletown, CT 06459, USA
Algebraic and Geometric Topology, Tome 8 (2008) no. 4, pp. 2401-2414
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We use Hopf rings to compute the homotopy rings π∗MO〈8〉 and π∗MU〈6〉 at primes  > 3. In this case, the additive structure is well-known, but the ring structure is not polynomial. Instead, these rings are quotients of polynomial rings by infinite regular sequences.

DOI : 10.2140/agt.2008.8.2401
Keywords: bordism, cobordism, String manifold, String bordism, Hopf ring

Hovey, Mark  1

1 Department of Mathematics and Computer Science, Wesleyan University, Middletown, CT 06459, USA 
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Hovey, Mark. The homotopy of MString and MU⟨6⟩ at large primes. Algebraic and Geometric Topology, Tome 8 (2008) no. 4, pp. 2401-2414. doi: 10.2140/agt.2008.8.2401

[1] M Ando, M J Hopkins, C Rezk, Multiplicative orientations of ${KO}$–theory and the spectrum of topological modular forms (2006)

[2] M Ando, M J Hopkins, N P Strickland, Elliptic spectra, the Witten genus and the theorem of the cube, Invent. Math. 146 (2001) 595

[3] J M Boardman, R L Kramer, W S Wilson, The periodic Hopf ring of connective Morava $K$–theory, Forum Math. 11 (1999) 761

[4] D Eisenbud, Commutative algebra with a view toward algebraic geometry, Graduate Texts in Math. 150, Springer (1995)

[5] S Glaz, Commutative coherent rings, Lecture Notes in Math. 1371, Springer (1989)

[6] M A Hovey, D C Ravenel, The $7$–connected cobordism ring at $p=3$, Trans. Amer. Math. Soc. 347 (1995) 3473

[7] N Kitchloo, G Laures, W S Wilson, The Morava $K$–theory of spaces related to $BO$, Adv. Math. 189 (2004) 192

[8] H Matsumura, Commutative ring theory, Cambridge Studies in Advanced Math. 8, Cambridge University Press (1989)

[9] D S C Morton, The Hopf ring for $b\mathrm{o}$ and its connective covers, J. Pure Appl. Algebra 210 (2007) 219

[10] D J Pengelley, The homotopy type of $M\mathrm{SU}$, Amer. J. Math. 104 (1982) 1101

[11] D C Ravenel, W S Wilson, The Hopf ring for complex cobordism, J. Pure Appl. Algebra 9 (1976) 241

[12] W S Wilson, The $\Omega $–spectrum for Brown–Peterson cohomology. II, Amer. J. Math. 97 (1975) 101

[13] E Witten, The index of the Dirac operator in loop space, from: "Elliptic curves and modular forms in algebraic topology (Princeton, NJ, 1986)" (editor P S Landweber), Lecture Notes in Math. 1326, Springer (1988) 161

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