An operadic model for a mapping space and its associated spectral sequence

ArticleJOURNAL OF PURE AND APPLIED ALGEBRA. 210(2): 321-342 (2007)journal articl

Iterated cyclic homology

ArticleKODAI MATHEMATICAL JOURNAL. 30(1): 19-40 (2007)journal articl

A function space model approach to the rational evaluation subgroups

The original publication is available at www.springerlink.com.ArticleMATHEMATISCHE ZEITSCHRIFT. 258(3): 521-555 (2008)journal articl

On hydrogen bond correlations at high pressures

In situ high pressure neutron diffraction measured lengths of O H and H O pairs in hydrogen bonds in substances are shown to follow the correlation between them established from 0.1 MPa data on different chemical compounds. In particular, the conclusion by Nelmes et al that their high pressure data on ice VIII differ from it is not supported. For compounds in which the O H stretching frequencies red shift under pressure, it is shown that wherever structural data is available, they follow the stretching frequency versus H O (or O O) distance correlation. For compounds displaying blue shifts with pressure an analogy appears to exist with improper hydrogen bonds.Comment: 12 pages,4 figure

Elastomeric spring actuator using nylon wires

Medical devices are designed for collaboration with the human body, which makes the steps to create them increasingly more complex if the device is to be implanted. Soft robots have the unique potential of meeting both the mechanical compliance with the interacting tissues and the controlled functionality needed for a repair or replacement. Soft devices that fulfill fundamental mechanical roles are needed as parts of soft robots in order to carry out desired tasks. As the medical devices become increasingly low-profile, soft devices must feature multi-functionality that is embedded in the structure. A device embedded with nylon actuators allows for the controlled collapsing of an elastomeric spring by compression alone or compression and twisting. In this paper we present the concept of a novel elastomeric spring, its fabrication and mechanical characterization

L-infinity algebra connections and applications to String- and Chern-Simons n-transport

We give a generalization of the notion of a Cartan-Ehresmann connection from Lie algebras to L-infinity algebras and use it to study the obstruction theory of lifts through higher String-like extensions of Lie algebras. We find (generalized) Chern-Simons and BF-theory functionals this way and describe aspects of their parallel transport and quantization. It is known that over a D-brane the Kalb-Ramond background field of the string restricts to a 2-bundle with connection (a gerbe) which can be seen as the obstruction to lifting the PU(H)-bundle on the D-brane to a U(H)-bundle. We discuss how this phenomenon generalizes from the ordinary central extension U(1) -> U(H) -> PU(H) to higher categorical central extensions, like the String-extension BU(1) -> String(G) -> G. Here the obstruction to the lift is a 3-bundle with connection (a 2-gerbe): the Chern-Simons 3-bundle classified by the first Pontrjagin class. For G = Spin(n) this obstructs the existence of a String-structure. We discuss how to describe this obstruction problem in terms of Lie n-algebras and their corresponding categorified Cartan-Ehresmann connections. Generalizations even beyond String-extensions are then straightforward. For G = Spin(n) the next step is "Fivebrane structures" whose existence is obstructed by certain generalized Chern-Simons 7-bundles classified by the second Pontrjagin class.Comment: 100 pages, references and clarifications added; correction to section 5.1 and further example to 9.3.1 adde