Related papers: I-adic towers in topology

We develop a operator algebraic model for twisted $K$-theory, which includes the most general twistings as a generalized cohomology theory (i.e. all those classified by the unit spectrum $bgl_1(KU)$). Our model is based on strongly…

We compute ko_*(K(Z/2,2)) and ko^*(K(Z/2,2)), the connective KO-homology and -cohomology of the mod 2 Eilenberg-MacLane space K(Z/2,2), using the Adams spectral sequence. The work relies heavily on work done several years earlier for the…

We use differential cohomology to systematically construct a large class of topological actions in physics, including Chern-Simons terms, Wess-Zumino-Novikov-Witten terms, and theta terms (continuous or discrete). We introduce a notion of…

This chapter sets out preliminaries for the duality theory in later chapters. An underlying idea is that local cohomology functors are higher derived functors of colocalizations (a.k.a.~coreflections). Predominantly well-known facts about…

We compute the $\mathrm{MU}$-based syntomic cohomologies, mod $(p,v_1,\cdots,v_{n})$, of all $\mathbb{E}_1$ $\mathrm{MU}$-algebra forms of the truncated Brown--Peterson spectrum $\mathrm{BP}\langle n\rangle$. As qualitative consequences, we…

This paper presents a commutative complex oriented cohomology theory with coefficients the quotient ring of complex cobordism MU$^*[1/2]$ modulo the ideal generated by any subsequence of any polynomial generators in special unitary…

We examine various versions of oriented cohomology and Borel-Moore homology theories in algebraic geometry and put these two together in the setting of an "oriented duality theory", a generalization of Bloch-Ogus twisted duality theory.…

We present an Eilenberg-Steenrod-like axiomatic framework for equivariant coarse homology and cohomology theories. We also discuss a general construction of such coarse theories from topological ones and the associated transgression maps. A…

We present a closed model structure for the category of pro-spectra in which the weak equivalences are detected by stable homotopy pro-groups. With some bounded-below assumptions, weak equivalences are also detected by cohomology as in the…

We prove two results regarding Hodge structures appearing in the cohomology of complex tori. First, we prove that if a polarizable Hodge structure appears in the cohomology of a complex torus $T$, it appears in the cohomology of an abelian…

Given a system of coverings of k-graphs, we show that the cohomology of the resulting (k+1)-graph is isomorphic to that of any one of the k-graphs in the system. We then consider Bratteli diagrams of 2-graphs whose twisted C*-algebras are…

Let X be a space, intended as a possibly curved spacetime, and A a precosheaf of C*-algebras on X. Motivated by algebraic quantum field theory, we study the Kasparov and Theta-summable K-homology of A interpreting them in terms of the…

The first part of the paper is a survey of recent results about the cohomology of $(\phi,\Gamma)$-modules and its applications to the theory of Selmer complexes. In the second part we formulate a version of the Main Conjecture for $p$-adic…

We describe the cohomology of the quotient Z_K/H of a moment-angle complex Z_K by a freely acting subtorus H in T^m by establishing a ring isomorphism of H*(Z_K/H,R) with an appropriate Tor-algebra of the face ring R[K], with coefficients…

Index maps taking values in the $K$-theory of a mapping cone are defined and discussed. The resulting index theorem can be viewed in analogy with the Freed-Melrose index theorem. The framework of geometric $K$-homology is used in a…

Let A be a commutative noetherian ring, and \a an ideal in it. In this paper we continue the study, begun in [PSY1], of the derived \a-adic completion and the derived \a-torsion functors. Here are our results: (1) a structural…

Let $\k$ be a commutative ring, and let $(A,\mfrak{a})$ be an adic ring which is a $\k$-algebra. We study complete and torsion versions of the derived Hochschild homology and cohomology functors of $A$ over $\k$. To do this, we first…

We set up a framework for using algebraic geometry to study the generalised cohomology rings that occur in algebraic topology. This idea was probably first introduced by Quillen and it underlies much of our understanding of complex oriented…

We found a quantum cohomology/homology of quantum Hall effect which arises as the invariant property of the Chern-Simons theory of quantum Hall effect and showed that it should be equivalent to the quantum cohomology which arose as the…

We dualise the classical fact that an operad with multiplication leads to cohomology groups which form a Gerstenhaber algebra to the context of cooperads: as a result, a cooperad with comultiplication induces a homology theory that is…