A Cayley map is a 2-cell embedding of a Cayley graph into an orientable surface with the same local orientation induced by a cyclic permutation of generators at each vertex. In this paper, we provide classifications of prime-valent regular Cayley maps on abelian groups, dihedral groups and dicyclic groups. Consequently, we show that all prime-valent regular Cayley maps on dihedral groups are ba...

BACKGROUND Assessment of cyclic myocardial blood flow (MBF) variations can be an interesting addition to the characterization of microvascular function and its alterations. To date, totally non-invasive in vivo methods with this capability are still lacking. As an original technique, a cine arterial spin labeling (ASL) cardiovascular magnetic resonance approach is demonstrated to be able to pro...

We present the construction of a Chern character in cyclic cohomology, involving an arbitrary number of associative algebras in contravariant or covariant position. This is a generalization of the bivariant Chern character for bornological algebras introduced in a previous paper [35], based on Quillen superconnections and heat-kernel regularization. Then we adapt the formalism to the cyclic coh...

We consider a one-parameter family of degree $d\ge 2$ rational maps with an automorphism group containing the cyclic order $d$. construct polynomial whose roots correspond to parameter values for which corresponding map is post-criticall

We determine the points of the epicyclic topos which plays a key role in the geometric encoding of cyclic homology and the lambda operations. We show that the category of points of the epicyclic topos is equivalent to projective geometry in characteristic one over algebraic extensions of the infinite semifield of “max-plus integers” Zmax. An object of this category is a pair (E,K) of a semimodu...

We consider a pairing producing various cyclic Hochschild cocycles, which led Alain Connes to cyclic cohomology. We are interested in geometrical meaning and homological properties of this pairing. We define a non-trivial pairing between the homology of a Lie-Rinehart (super-)algebra with coefficients in some partial traces and relative periodic cyclic homology. This pairing generalizes the ind...