Related papers: Explicit Wodzicki excision in cyclic homology

Using the technique of Poincar\'{e} return maps, we disclose an intricate order of the subsequent homoclinics near the primary homoclinic bifurcation of the Shilnikov saddle-focus in systems with reflection symmetry. We also reveal the…

We prove that rigid representations of the fundamental group of a surface into the group of oreintation-preserving homeomorphisms of the circle are geometric, thereby establishing a converse statement of a theorem by the first author.

We study open-closed discrete mappings that satisfy the weighted estimate of the distortion of modulus of families of paths. It is proved that the mappings mentioned above have a continuous extension into the isolated point of the boundary,…

We review recent progress in the study of cyclic cohomology of Hopf algebras, Hopf algebroids, and invariant cyclic homology starting with the pioneering work of Connes-Moscovici.

In this expository paper we present some ideas of algebraic topology (more precisely, of homology theory) in a language accessible to non-specialists in the area. A $1$-cycle in a graph is a set $C$ of edges such that every vertex is…

We describe a way to compute mapping spaces of cyclic operads through modules. As an application we compute the homotopy automorphism space of the cyclic Batalin-Vilkovisky (Hopf co-)operad.

Based on various strategies and a new general doubling operator, we obtain several simple proofs of the celebrated Sharkovsky's cycle coexistence theorem. A simple non-directed graph proof which is especially suitable for a calculus course…

We provide an alternative, simpler proof of the existence of thick triangulations for noncompact $\mathcal{C}^1$ manifolds. Moreover, this proof is simpler than the original one given in \cite{pe}, since it mainly uses tools of elementary…

In this paper we initiate the study of cyclic algebraic geometry codes. We give conditions to construct cyclic algebraic geometry codes in the context of algebraic function fields over a finite field by using their group of automorphisms.…

We present an elementary derivation of the period-three cycles for the real quadratic map $x\mapsto x^2+c$, a fundamental model in one-dimensional discrete dynamics. Using symmetric polynomials, we obtain a complete algebraic…

In this paper we present an unconditional proof of Wojtkowski's Ergodicity Conjecture for almost every system of 1D perfectly elastic balls falling down in a half line under constant gravitational acceleration. Namely, by introducing a new…

We construct exponential maps for which the singular value tends to infinity under iterates while the maps are ergodic. This is in contrast with a result of Lyubich from 1987 which tells that $e^z$ is not ergodic.

In this short note, we prove the uniqueness of exterior differentiation on locally finite graphs.

Chessboard complexes and their relatives have been one of important recurring themes of topological combinatorics. Closely related ``cycle-free chessboard complexes'' have been recently introduced by Ault and Fiedorowicz as a tool for…

We find an explicit form of the inverse isomorphism from Shapiro's lemma in terms of inhomogeneous cocycles and apply it to construct special nonsplit coverings of groups with a unique conjugacy class of involutions.

This paper investigates the admissibility of the substitution rule in cyclic-proof systems. The substitution rule complicates theoretical case analysis and increases computational cost in proof search since every sequent can be a conclusion…

We define a new cyclic module, dual to the Connes-Moscovici cyclic module, for Hopf algebras, and give a characteristric map for the coaction of Hopf algebras. We also compute the resulting cyclic homology for cocommutative Hopf algebras,…

We introduce a class of cycles, called nondegenerate, strictly decomposable cycles, and show that the image of each cycle in this class under the refined cycle map to an extension group in the derived category of arithmetic mixed Hodge…

The main result of this paper is a proof using real analysis of the monotonicity of the topological entropy for the family of quadratic maps, sometimes called Milnor's Monotonicity Conjecture. In contrast, the existing proofs rely in one…

The aim of this note is to show that the generalized supertrace, constructed in another paper of the author, inducing an isomorphism between the Hochschild homology of a superalgebra and that of the superalgebra of square supermatrices of a…