Showing papers in "Topology in 1965"

TL;DR: In this article, it was shown that the only physically meaningful description of a state was in terms of an assignment of probability measures to the spectra of the observables (a measurement of the observable with the system in a given state will produce a value in a specific portion of the spectrum with a specific probability).

TL;DR: In this paper, the Lefschetz fixed point theorem has been transformed into an algebraic version of the Nielsen-Wecken fixed point theory, and it has been shown that the center of the fundamental group of a finite, aspherical polyhedron whose Euler characteristic is non-zero is trivial.

TL;DR: In this paper, it was shown that if n = 2' + 3, r 2 3, then P*-l and P(n) do not immerse in R2'-7.

TL;DR: In this article, the authors give a homotopy theoretic criterion for an imbedding of the n-sphere s into a higher dimension msphere to be "equivalent" to the standard imbding.

TL;DR: In this article, the authors characterize those cobordism classes in the Thom ring N ∗ and Ω ∗ which contain complex manifolds and attempt to characterize those classes in N ∆ which contain spin manifolds.

TL;DR: In this article, the authors consider the problem of the projection of a bounded operator on a real or complex Hilbert space into a subalgebra of bounded operators on the subspace H, spanned by {eI,...,, e,}.

TL;DR: In this article, the authors considered the problem of finding a resolution (1) in which fO, Fi, Z is ZG-free on fO generators, where the conditions on the fi are a set of inequalities connecting them with cohomological invariants of G.

TL;DR: In this paper, the authors generalize the Whitehead product by replacing the wedge of two spheres with a "wedge" of n suspensions, which is a generalization of the original 2"d order Whitehead products.

TL;DR: In this paper, the authors present a new technique for constructing knots, also based on a prescription of linking information, which can resolve the problem of algebraic characterisation of higher-dimensional knots.

TL;DR: In this article, a manifold of real dimension n whose stable tangent bundle admits a reduction to the stable groups U, SO, SU, Spin, or Spin' is defined, and classification defines a map M + BG and composing H(BG, Q) --, H(M, Q).

TL;DR: In this paper, it was shown that the algebra of (Maurer-Cartan) complex-valued left invariant differential forms may be naturally identified with the exterior algebra of a compact semi-simple Lie group.

TL;DR: In this article, it was shown that C is also homotopy equivalent to the covering space of K determined by the subgroup h,n,(C) of n,(K).

TL;DR: In this paper, the authors studied diagonal operations, a new class of secondary cohomology operations of several variables, including the Massey triple and n-ary products, which were introduced and studied in the context of mod p Steenrod algebra.

TL;DR: In this article, it was shown that a polyhedral polyhedron X is said to be unknotted in another polyhedral sphere Y if any two piecewise linear embeddings of X and Y that are homotopic are also ambient isotopic; this means that one embedding can be carried to the other by a piece wise linear isotopy of Y.

TL;DR: In this article, the authors define K, and K1 in a context sufficiently broad to subsume the several cases of K. What appears to be necessary is a category together with some notion of "extension" of a pair of objects.

TL;DR: In this paper, the authors studied the possible distributions of numbers at which certain meromorphic functions take on algebraic values, and showed that a 1-parameter subgroup of a linear group or an abelian variety which contains sufficiently many algebraic points must itself be an algebraic subgroup.