A Filtration of the Loops on SU (N) by Schubert Varieties.
A fixed point index for bimaps
A Fixed Point Index Theory for Symmetric Product Mappings.
A fixed point theorem in o-minimal structures
Here we prove an o-minimal fixed point theorem for definable continuous maps on definably compact definable sets, generalizing Brumfiel’s version of the Hopf fixed point theorem for semi-algebraic maps.
A fixed-point theorem for homeomorphisms of
A formula for the rational LS-category of certain spaces
In this paper we find a formula for the rational LS-category of certain elliptic spaces which generalizes or complements previous work of the subject. This formula is given in terms of the minimal model of the space.
A formula for topology/deformations and its significance
The formula is , with ∂a + 1/2 [a,a] = 0 and ∂b + 1/2 [b,b] = 0, where a, b and e in degrees -1, -1 and 0 are the free generators of a completed free graded Lie algebra L[a,b,e]. The coefficients are defined by . The theorem is that ∙ this formula for ∂ on generators extends to a derivation of square zero on L[a,b,e]; ∙ the formula for ∂e is unique satisfying the first property, once given the formulae for ∂a and ∂b, along with the condition that the “flow” generated by e moves a to b in unit...
A functional S-dual in a strong shape category
In the S-category (with compact-open strong shape mappings, cf. §1, instead of continuous mappings, and arbitrary finite-dimensional separable metrizable spaces instead of finite polyhedra) there exists according to [1], [2] an S-duality. The S-dual , turns out to be of the same weak homotopy type as an appropriately defined functional dual (Corollary 4.9). Sometimes the functional object is of the same weak homotopy type as the “real” function space (§5).
A Functorial Construction of Fibre Bundles with a Structural Group
A -minimal model for principal -bundles
Sullivan associated a uniquely determined to any simply connected simplicial complex . This algebra (called minimal model) contains the total (and exactly) rational homotopy information of the space . In case is the total space of a principal -bundle, ( is a compact connected Lie-group) we associate a -equivariant model , which is a collection of “-homotopic” ’s with -action. will, in general, be different from the Sullivan’s minimal model of the space . contains the total rational...
A Galois theory with stable units for simplicial sets.
A general approximation theorem for Hilbert cube manifolds
A generalization of cohomotopy groups
A generalization of contraction principle.
A Generalization of the Lambda Algebra.
A Generalized Mean-Value Theorem.
A geometric decomposition of spaces into cells of different types.
A geometric description of differential cohomology
In this paper we give a geometric cobordism description of differential integral cohomology. The main motivation to consider this model (for other models see [5, 6, 7, 8]) is that it allows for simple descriptions of both the cup product and the integration. In particular it is very easy to verify the compatibilty of these structures. We proceed in a similar way in the case of differential cobordism as constructed in [4]. There the starting point was Quillen’s cobordism description of singular cobordism...
A higher dimensional homotopy sequence.
A homological selection theorem implying a division theorem for Q-manifolds
We prove that a space M with Disjoint Disk Property is a Q-manifold if and only if M × X is a Q-manifold for some C-space X. This implies that the product M × I² of a space M with the disk is a Q-manifold if and only if M × X is a Q-manifold for some C-space X. The proof of these theorems exploits the homological characterization of Q-manifolds due to Daverman and Walsh, combined with the existence of G-stable points in C-spaces. To establish the existence of such points we prove (and afterward...