-homotopy theory of schemes
A 2-category of chronological cobordisms and odd Khovanov homology
We create a framework for odd Khovanov homology in the spirit of Bar-Natan's construction for the ordinary Khovanov homology. Namely, we express the cube of resolutions of a link diagram as a diagram in a certain 2-category of chronological cobordisms and show that it is 2-commutative: the composition of 2-morphisms along any 3-dimensional subcube is trivial. This allows us to create a chain complex whose homotopy type modulo certain relations is a link invariant. Both the original and the odd Khovanov...
A Based Federer Spectral Sequence and the Rational Homotopy of Function Spaces.
A base-point-free definition of the Lefschetz invariant.
A Bing-Borsuk retract which contains a 2-dimensional absolute retract [Book]
A Bound for the Fixed-Point Index of an Area-Preserving Map with Applications to Mechanics.
A calculation of Pin+ Bordism groups.
A Cech-Hurewicz Isomorphism Theorem for Movable Metric Compacta.
A Cellular Construction of BP and Other Irreducible Spectra.
A Chain Level Transfer Homomorphism.
A chain rule in the calculus of homotopy functors.
A characterization of harmonic sections and a Liouville theorem
Let be a principal fiber bundle and an associated fiber bundle. Our interest is to study the harmonic sections of the projection of into . Our first purpose is give a characterization of harmonic sections of into regarding its equivariant lift. The second purpose is to show a version of a Liouville theorem for harmonic sections of .
A characterization of MAR and MANR-spaces by extendability of mutations
A characterization of movable compacta.
A Chen model for mapping spaces and the surface product
We develop a machinery of Chen iterated integrals for higher Hochschild complexes. These are complexes whose differentials are modeled on an arbitrary simplicial set much in the same way the ordinary Hochschild differential is modeled on the circle. We use these to give algebraic models for general mapping spaces and define and study the surface product operation on the homology of mapping spaces of surfaces of all genera into a manifold. This is an analogue of the loop product in string topology....
A Class of C*-algebras and Topological Markov Chains II: Reducible Chains and the Ext-functor for C*-algebras.
A classification of cohomology transfers for ramified covering maps
We construct a cohomology transfer for n-fold ramified covering maps. Then we define a very general concept of transfer for ramified covering maps and prove a classification theorem for such transfers. This generalizes Roush's classification of transfers for n-fold ordinary covering maps. We characterize those representable cofunctors which admit a family of transfers for ramified covering maps that have two naturality properties, as well as normalization and stability. This is analogous to Roush's...
A classification of polynomial algebras as modules over the Steenrod algebra.
A classification of secondary cohomology operations
A classification of small homotopy functors from spectra to spectra
We show that every small homotopy functor from spectra to spectra is weakly equivalent to a filtered colimit of representable functors represented in cofibrant spectra. Moreover, we present this classification as a Quillen equivalence of the category of small functors from spectra to spectra equipped with the homotopy model structure and the opposite of the pro-category of spectra with the strict model structure.