The homotopy of MString and MU〈6〉 at large primes
نویسندگان
چکیده
Recall that a String manifold is a Spin manifold M together with a trivialization of the class usually denoted p1(M)/2; this is a characteristic class, defined only for Spin manifolds, so that twice it is the usual first Pontrjagin class. The bordism spectrum of String manifolds is called MString or MO〈8〉; it is the Thom spectrum of the map BO〈8〉 −→ BO of the 7-connected cover of BO to BO. Similarly, MU〈6〉 is the bordism spectrum associated with the 5-connected cover BU〈6〉 −→ BU of BU .
منابع مشابه
Homotopy Exponents for Large H-spaces
We show that H-spaces with finitely generated cohomology, as an algebra or as an algebra over the Steenrod algebra, have homotopy exponents at all primes. This provides a positive answer to a question of Stanley.
متن کاملThe Cohomology of the Height Four Morava Stabilizer Group at Large Primes
This is an announcement of some new computational methods in stable homotopy theory, in particular, methods for using the cohomology of small-height Morava stabilizer groups to compute the cohomology of large-height Morava stabilizer groups. As an application, the cohomology of the height four Morava stabilizer group is computed at large primes (its rank turns out to be 3440). Consequently we a...
متن کاملThe Homotopy Type of a Poincaré Duality Complex after Looping
We given an answer to a weaker version of the classification problem for the homotopy types of (n − 2)-connected closed orientable (2n − 1)-manifolds. Let n ≥ 6 be an even integer, and X be a (n − 2)-connected finite orientable Poincaré (2n − 1)-complex. Then for odd primes p, its loop space homotopy type after localizing at p is uniquely determined by Hn−1(X; Q), and the action of the Bockstei...
متن کاملAN ALGORITHM FOR FINDING THE EIGENPAIRS OF A SYMMETRIC MATRIX
The purpose of this paper is to show that ideas and techniques of the homotopy continuation method can be used to find the complete set of eigenpairs of a symmetric matrix. The homotopy defined by Chow, Mallet- Paret and York [I] may be used to solve this problem with 2""-n curves diverging to infinity which for large n causes a great inefficiency. M. Chu 121 introduced a homotopy equation...
متن کاملOn the Nilpotence Order of β 1
For p > 2, β1 ∈ π 2p2−2p−2(S) is the first positive even-dimensional element in the stable homotopy groups of spheres. A classical theorem of Nishida [Nis73] states that all elements of positive dimension in the stable homotopy groups of spheres are nilpotent. In fact, Toda [Tod68] proved β 2−p+1 1 = 0. For p = 3 he showed that β 1 = 0 while β 5 1 6= 0. In [Rav86] the second author computed the...
متن کامل