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53
On the nonexistence of elements of Hopf invariant one
 Ann. of Math
, 1960
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Cited by 69 (0 self)
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JSTOR is a notforprofit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. Annals of Mathematics is collaborating with JSTOR to digitize, preserve and extend access to The Annals of Mathematics.
The compression theorem
 I., Geom. Topol
"... This the first of a set of three papers about the Compression Theorem: if M m is embedded in Q q × R with a normal vector field and if q − m ≥ 1, then the given vector field can be straightened (ie, made parallel to the given R direction) by an isotopy of M and normal field in Q × R. The theorem can ..."
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Cited by 21 (9 self)
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This the first of a set of three papers about the Compression Theorem: if M m is embedded in Q q × R with a normal vector field and if q − m ≥ 1, then the given vector field can be straightened (ie, made parallel to the given R direction) by an isotopy of M and normal field in Q × R. The theorem can be deduced from Gromov’s theorem on directed embeddings [5; 2.4.5 (C ′)] and is implicit in the preceeding discussion. Here we give a direct proof that leads to an explicit description of the finishing embedding. In the second paper in the series we give a proof in the spirit of Gromov’s proof and in the third part we give applications.
Some Results in Geometric Topology and Geometry”, Thesis submitted for the degree
 of PhD, Warwick Maths Institute
, 1997
"... ..."
Homotopy theory of the suspensions of the projective plane
 Memoirs AMS
"... Abstract. The homotopy theory of the suspensions of the real projective plane is largely investigated. The homotopy groups are computed up to certain range. The decompositions of the self smashes and the loop spaces are studied with some applications to the Stiefel manifolds. ..."
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Cited by 12 (8 self)
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Abstract. The homotopy theory of the suspensions of the real projective plane is largely investigated. The homotopy groups are computed up to certain range. The decompositions of the self smashes and the loop spaces are studied with some applications to the Stiefel manifolds.
The polyhedral product functor: a method of computation for momentangle complexes, arrangements and related spaces
, 2008
"... This article gives a natural decomposition of the suspension of generalized momentangle complexes or partial product spaces which arise as polyhedral product functors described below. In the special case of the complements of certain subspace arrangements, the geometrical decomposition implies the ..."
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Cited by 12 (2 self)
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This article gives a natural decomposition of the suspension of generalized momentangle complexes or partial product spaces which arise as polyhedral product functors described below. In the special case of the complements of certain subspace arrangements, the geometrical decomposition implies the homological decomposition in GoreskyMacPherson [20], Hochster[22], Baskakov [3], Panov [36], and BuchstaberPanov [7]. Since the splitting is geometric, an analogous homological decomposition for a generalized momentangle complex applies for any homology theory. This decomposition gives an additive decomposition for the StanleyReisner ring of a finite simplicial complex and generalizations of certain homotopy theoretic results of Porter [39] and Ganea [19]. The spirit of the work here follows that of DenhamSuciu in [16].
On Maps From Loop Suspensions To Loop Spaces And The Shuffle Relations On The Cohen Groups
"... The maps from loop suspensions to loop spaces are investigated using group representations in this article. The shuffle relations on the Cohen groups are given. By using these relations, a universal ring for functorial self maps of double loop spaces of double suspensions is given. Moreover the obst ..."
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Cited by 9 (8 self)
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The maps from loop suspensions to loop spaces are investigated using group representations in this article. The shuffle relations on the Cohen groups are given. By using these relations, a universal ring for functorial self maps of double loop spaces of double suspensions is given. Moreover the obstructions to the classical exponent problem in homotopy theory are displayed in the extension groups of the dual of the important symmetric group modules Lie(n), as well as in the top cohomology of the Artin braid groups with coefficients in the top homology of the Artin pure braid groups.
A HAEFLIGER STYLE DESCRIPTION OF THE EMBEDDING CALCULUS TOWER
"... Abstract. Let M and N be smooth manifolds. The calculus of embeddings produces, for every k ≥ 1, a best degree ≤ k polynomial approximation to the cofunctor taking an open V ⊂ M to the space of embeddings from V to N. In this paper a description of these polynomial approximations in terms of equivar ..."
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Cited by 7 (1 self)
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Abstract. Let M and N be smooth manifolds. The calculus of embeddings produces, for every k ≥ 1, a best degree ≤ k polynomial approximation to the cofunctor taking an open V ⊂ M to the space of embeddings from V to N. In this paper a description of these polynomial approximations in terms of equivariant mapping spaces is given, for k ≥ 2. The description is new only for k ≥ 3. In the case k = 2 we recover Haefliger’s approximation and the known result that it is the best degree ≤ 2 approximation. Let M and N be smooth manifolds, without boundary for simplicity, dim(M) = m and dim(N) = n where n> 3. The calculus of embeddings [10], [11], [3], [2] produces certain ‘Taylor ’ approximations Tkemb(M, N) to the space emb(M, N) of smooth embeddings from M to N. In more detail, there are maps
An elementary construction of Anick’s fibration, submitted
"... Abstract. Cohen, Moore, and Neisendorfer’s work on the odd primary homotopy theory of spheres and Moore spaces, as well as the first author’s work on the secondary suspension, predicted the existence of a plocal fibration S2n−1 − → T − → ΩS2n+1 whose connecting map is degree pr. In a long and compl ..."
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Cited by 6 (5 self)
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Abstract. Cohen, Moore, and Neisendorfer’s work on the odd primary homotopy theory of spheres and Moore spaces, as well as the first author’s work on the secondary suspension, predicted the existence of a plocal fibration S2n−1 − → T − → ΩS2n+1 whose connecting map is degree pr. In a long and complex monograph, Anick constructed such a fibration for p ≥ 5 and r ≥ 1. Using new methods we give a much more conceptual construction which is also valid for p = 3 and r ≥ 1. We go on to establish several properties of the space T. 1.
ON SYMMETRIC COMMUTATOR SUBGROUPS, BRAIDS, LINKS AND HOMOTOPY GROUPS
"... Abstract. In this paper, we investigate some applications of commutator subgroups to homotopy groups and geometric groups. In particular, we show that the intersection subgroups of some canonical subgroups in certain link groups modulo their symmetric commutator subgroups are isomorphic to the (high ..."
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Cited by 6 (5 self)
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Abstract. In this paper, we investigate some applications of commutator subgroups to homotopy groups and geometric groups. In particular, we show that the intersection subgroups of some canonical subgroups in certain link groups modulo their symmetric commutator subgroups are isomorphic to the (higher) homotopy groups. This gives a connection between links and homotopy groups. Similar results hold for braid and surface groups. 1.