Codimension one immersions and the Kervaire invariant one problem
نویسنده
چکیده
منابع مشابه
The Kervaire invariant of immersions
where f2. G is an appropriate cobordism theory of immersed submanifolds of Euclidean space. By generalizing techniques of Browder [2] we shall give necessary and sufficient Adams spectral sequence conditions for an element in t2. G to have nonzero Kervaire invariant. Also we will prove that for every j > 1 there exists a closed, differentiable manifold of dimension 2 ) § together with an immers...
متن کاملA geometrical proof of Browder ' s result on the vanishing of theKervaire
The Kervaire invariant is a Z=2-invariant of framed manifolds of dimension n = 4k + 2. W. Browder proved 5] that this invariant necessarily vanishes if n + 2 is not a power of 2. We give a geometrical proof of this result using a characterization of the Kervaire invariant in terms of multiple points of immersions.
متن کاملOn the Non-existence of Elements of Kervaire Invariant One
We show that the Kervaire invariant one elements θj ∈ π2j+1−2S 0 exist only for j ≤ 6. By Browder’s Theorem, this means that smooth framed manifolds of Kervaire invariant one exist only in dimensions 2, 6, 14, 30, 62, and possibly 126. Except for dimension 126 this resolves a longstanding problem in algebraic topology.
متن کاملar X iv : 0 90 8 . 37 24 v 1 [ m at h . A T ] 2 6 A ug 2 00 9 ON THE NON - EXISTENCE OF ELEMENTS OF KERVAIRE INVARIANT ONE
We show that the Kervaire invariant one elements θj ∈ π2j+2−2S 0 exist only for j ≤ 6. By Browder’s Theorem, this means that smooth framed manifolds of Kervaire invariant one exist only in dimensions 2, 6, 14, 30, 62, and possibly 126. Except for dimension 126 this resolves a longstanding problem in algebraic topology.
متن کاملThe Kervaire invariant and surgery theory
We give an expository account of the development of the Kervaire invariant and its generalizations with emphasis on its applications to surgery and, in particular, to the existence of stably parallelizable manifolds with Kervaire invariant one.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1981