The circle action on topological Hochschild homology of complex cobordism and the Brown-Peterson spectrum

We specify exterior generators for $\pi_* THH(MU) = \pi_*(MU) \otimes E(\lambda'_n \mid n\ge1)$ and $\pi_* THH(BP) = \pi_*(BP) \otimes E(\lambda_n \mid n\ge1)$, and calculate the action of the $\sigma$-operator on these graded rings. In particular, $\sigma(\lambda'_n) = 0$ and $\sigma(\lambda_n) = 0$, while the actions on $\pi_*(MU)$ and $\pi_*(BP)$ are expressed in terms of the right units $\eta_R$ in the Hopf algebroids $(\pi_*(MU), \pi_*(MU \wedge MU))$ and $(\pi_*(BP), \pi_*(BP \wedge BP))$, respectively.Comment: This paper has been accepted for publication by the Journal of Topolog

Stably dualizable groups

We extend the duality theory for topological groups from the classical theory for compact Lie groups, via the topological study by J. R. Klein [Kl01] and the p-complete study for p-compact groups by T. Bauer [Ba04], to a general duality theory for stably dualizable groups in the E-local stable homotopy category, for any spectrum E. The principal new examples occur in the K(n)-local category, where the Eilenberg-Mac Lane spaces G = K(Z/p, q) are stably dualizable and nontrivial for 0 <= q <= n. We show how to associate to each E-locally stably dualizable group G a stably defined representation sphere S^{adG}, called the dualizing spectrum, which is dualizable and invertible in the E-local category. Each stably dualizable group is Atiyah-Poincare self-dual in the E-local category, up to a shift by S^{adG}. There are dimension-shifting norm- and transfer maps for spectra with G-action, again with a shift given by S^{adG}. The stably dualizable group G also admits a kind of framed bordism class [G] in pi_*(L_E S), in degree dim_E(G) = [S^{adG}] of the Pic_E-graded homotopy groups of the E-localized sphere spectrum.Comment: Final version, to appear in the Memoirs of the A.M.

Algebraic K-theory of strict ring spectra

We view strict ring spectra as generalized rings. The study of their algebraic K-theory is motivated by its applications to the automorphism groups of compact manifolds. Partial calculations of algebraic K-theory for the sphere spectrum are available at regular primes, but we seek more conceptual answers in terms of localization and descent properties. Calculations for ring spectra related to topological K-theory suggest the existence of a motivic cohomology theory for strictly commutative ring spectra, and we present evidence for arithmetic duality in this theory. To tie motivic cohomology to Galois cohomology we wish to spectrally realize ramified extensions, which is only possible after mild forms of localization. One such mild localization is provided by the theory of logarithmic ring spectra, and we outline recent developments in this area.Comment: Contribution to the proceedings of the ICM 2014 in Seou

Telecommuting resistance, soft but strong: Development of telecommuting over time, and related rhetoric, in three organisations

Telecommuting, or working part of the time from another location than the office, normally from home, has been tried by several organisations in the recent years. This has not always been a success. Still, many arguments in favour of telecommuting are forwarded by previous studies. This paper investigates the development of telecommuting in three organisations, and elaborates on mechanisms behind the fact that the practice of telecommuting has not been as widespread as expected. The study is longitudinal, covering three years, and mainly based on interviews. The practice of telecommuting is found to have a negative development over time in all three cases. The social/symbolic aspects are found to be strong, but initially not reflected upon by the organisations. Many arguments in early phases of telecommuting are of a rational/functional nature, and tend to treat work as an output-related activity, without considering social and symbolic aspects of distancing oneself from the worksite and the colleagues. Over time, symbolic aspects become more pronounced. This complements/overrides the rational/functional arguments initially used by those in favour of telecommuting. This shift over time needs to be taken into account to understand the initial positive response to, but difficulties to sustain telecommuting.Telework; telecommuting; Geographical dispersion; Organisation

Organising R&D in a global environment, Increasing dispersed co-operation versus continuos centralisation.

Theories on R&D organisation draw on globalisation literature as well as on communication theories. This mixed discourse is a problem, since mixing levels of logic sometimes cause faulty conclusions. How is this double logic handled in organisations, and what is the effect on R&D organisation? This study investigates R&D activities in multinational companies with several production sites and markets, focusing what reasons and forces are mentioned in relation to the geographical structure of the R&D activities. We assume that there are opposing forces, both dispersing and contracting the R&D activities geographically. The purpose of the paper is to investigate perceived geographically dispersing and contracting forces on R&D activities, and how a possible conflict between these is handled. This is done by studying how the level of dispersion has come to be, what events or decision has caused the dispersion of R&D. We show that trends in R&D dispersion are active in two directions, one dispersing and one contracting, and that these are partly working at separate organisational levels. The dispersing forces are more prevalent at strategic levels, while the contracting forces are more pronounced at the operational level.R&D; Globalization; Communication; Virtual teams

Geographical dispersion and spontaneous interaction in an R&D environment

This study investigates how spontaneous interaction in an R&D environment is affected by temporary absence form the work site. Previous studies has shown the central importance of spontaneous interaction in R&D activities, but not how this is linked to the amount of co-presence. By using work diaries to collect data on time spent on spontaneous interaction, two groups are studied, one working form a remote location for part of the time, and one working at the central location all the time. The assumption is that spontaneous interaction is either constant during time of co-presence, or it is saved until time of presence. In the later case this would result in more spontaneous interaction when present. The results from the study show that the spontaneous interaction is directly linked to the amount of time the person is present, and that no compensation is made for the time of absence. Spontaneous interaction takes place when opportunities occur, and lost opportunities are not compensated for by more spontaneous interaction when opportunity is given later. This has implications for geographical dispersion in environments where spontaneous interaction is vital such as in R&D settings and in managerial roles. Part-time geographical separation will decrease the amount of spontaneous interaction in the group, which is likely to influence the outcome.Communication; Telecommuting; R&D; Social interaction

Hopf algebra structure on topological Hochschild homology

The topological Hochschild homology THH(R) of a commutative S-algebra (E_infty ring spectrum) R naturally has the structure of a commutative R-algebra in the strict sense, and of a Hopf algebra over R in the homotopy category. We show, under a flatness assumption, that this makes the Boekstedt spectral sequence converging to the mod p homology of THH(R) into a Hopf algebra spectral sequence. We then apply this additional structure to the study of some interesting examples, including the commutative S-algebras ku, ko, tmf, ju and j, and to calculate the homotopy groups of THH(ku) and THH(ko) after smashing with suitable finite complexes. This is part of a program to make systematic computations of the algebraic K-theory of S-algebras, by means of the cyclotomic trace map to topological cyclic homology.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-49.abs.htm

Algebraic K-theory of the first Morava K-theory

We compute the algebraic K-theory modulo p and v_1 of the S-algebra ell/p = k(1), using topological cyclic homology.Comment: Revised version, to appear in J. Eur. Math. Soc. (JEMS