Existence of weak homotopy equivalences between spectra for U-bordism with singularities
Extensions of umbral calculus II: double delta operators, Leibniz extensions and Hattori-Stong theorems
We continue our programme of extending the Roman-Rota umbral calculus to the setting of delta operators over a graded ring with a view to applications in algebraic topology and the theory of formal group laws. We concentrate on the situation where is free of additive torsion, in which context the central issues are number- theoretic questions of divisibility. We study polynomial algebras which admit the action of two delta operators linked by an invertible power series, and make related constructions...
Fibrations and homology sphere bordism.
Forms of K-Theory.
Framed bicobordism
Galois theory and Lubin-Tate cochains on classifying spaces
We consider brave new cochain extensions F(BG +,R) → F(EG +,R), where R is either a Lubin-Tate spectrum E n or the related 2-periodic Morava K-theory K n, and G is a finite group. When R is an Eilenberg-Mac Lane spectrum, in some good cases such an extension is a G-Galois extension in the sense of John Rognes, but not always faithful. We prove that for E n and K n these extensions are always faithful in the K n local category. However, for a cyclic p-group , the cochain extension is not a Galois...
Generators of the unoriented bordism ring which are fibered over products of projective spaces RP(2r-1).
Homology cobordism group of homology 3-spheres.
Homology of braid groups and their generalizations
In the paper we give a survey of (co)homologies of braid groups and groups connected with them. Among these groups are pure braid groups and generalized braid groups. We present explicit formulations of some theorems of V. I. Arnold, E. Brieskorn, D. B. Fuks, F. Cohen, V. V. Goryunov and others. The ideas of some proofs are outlined. As an application of (co)homologies of braid groups we study the Thom spectra of these groups.
-adic towers in topology.
-local Johnson-Wilson spectra and their Hopf algebroids.
Injective comodules and Landweber exact homology theories
We classify the indecomposable injective E(n)⁎E(n)-comodules, where E(n) is the Johnson-Wilson homology theory. They are suspensions of the , where 0 ≤ r ≤ n, with the endomorphism ring of being , where denotes the completion of E(r).
Lokalisierung äquivarianter Kohomologie-Theorien.
Modules de -bordisme. Couples exacts cohérents
Modules de -bordisme. -résolutions de complexes finis
Modules de SU-bordisme. Applications
Motivic Landweber exactness.
Multiplicative operations in the Steenrod algebra for Brown–Peterson cohomology
A family of multiplicative operations in the BP Steenrod algebra is defined which is related to the total Steenrod power operation from the mod p Steenrod algebra. The main result of the paper links the BP versions of the total Steenrod power with the formal group approach to multiplicative BP operations by identifying the p-typical curves (power series) which correspond to these operations. Some relations are derived from this identification, and a short proof of the Hopf invariant one theorem...
On resolving singularities and relating bordism to homology
On symplectic cobordism of real projective plane.
This note answers a question of V. V. Vershinin concerning the properties of Buchstaber's elements Θ2i+1(2) in the symplectic cobordism ring of the real projective plane. It is motivated by Roush's famous result that the restriction of these elements to the projective line is trivial, and by the relationship with obstructions to multiplication in symplectic cobordism with singularities.