Stable concordance of knots in 3-manifolds

Knots and links in 3-manifolds are studied by applying intersection invariants to singular concordances. The resulting link invariants generalize the Arf invariant, the mod 2 Sato-Levine invariants, and Milnor's triple linking numbers. Besides fitting into a general theory of Whitney towers, these invariants provide obstructions to the existence of a singular concordance which can be homotoped to an embedding after stabilization by connected sums with $S^2\times S^2$. Results include classifications of stably slice links in orientable 3-manifolds, stable knot concordance in products of an orientable surface with the circle, and stable link concordance for many links of null-homotopic knots in orientable 3-manifolds.Comment: 59 pages, 28 figure

Whitney tower concordance of classical links

This paper computes Whitney tower filtrations of classical links. Whitney towers consist of iterated stages of Whitney disks and allow a tree-valued intersection theory, showing that the associated graded quotients of the filtration are finitely generated abelian groups. Twisted Whitney towers are studied and a new quadratic refinement of the intersection theory is introduced, measuring Whitney disk framing obstructions. It is shown that the filtrations are completely classified by Milnor invariants together with new higher-order Sato-Levine and higher-order Arf invariants, which are obstructions to framing a twisted Whitney tower in the 4-ball bounded by a link in the 3-sphere. Applications include computation of the grope filtration, and new geometric characterizations of Milnor's link invariants.Comment: Only change is the addition of this comment: This paper subsumes the entire preprint "Geometric Filtrations of Classical Link Concordance" (arXiv:1101.3477v2 [math.GT]) and the first six sections of the preprint "Universal Quadratic Forms and Untwisting Whitney Towers" (arXiv:1101.3480v2 [math.GT]

Some theory of bivariate risk attitude

In past years the study of the impact of risk attitude among risks has become a major topic, in particular in Decision Sciences. Subsequently the attention was devoted to the more general case of bivariate random variables. The first approach to multivariate risk aversion was proposed by de Finetti (1952) and Richard (1975) and it is related to the bivariate case. More recently, multivariate risk aversion has been studied by Scarsini (1985, 1988, 1999). Nevertheless even if decision problems with consequences described by more than two attributes have become increasingly important, some questions appear not completely solved. This paper concerns with a definition of bivariate risk aversion which is related to a particular type of concordance: a bivariate risk averse Decision Maker is a Decision Maker who always prefers the independent version of a bivariate random variable to the random variable itself.Bivariate risk aversion; concordance aversion; submodular functions; bivariate association; concordance; dependence; diversification.

The Selection Function of SZ Cluster Surveys

We study the nature of cluster selection in Sunyaev-Zel'dovich (SZ) surveys, focusing on single frequency observations and using Monte Carlo simulations incorporating instrumental effects, primary cosmic microwave background (CMB) anisotropies and extragalactic point sources. Clusters are extracted from simulated maps with an optimal, multi-scale matched filter. We introduce a general definition for the survey selection function that provides a useful link between an observational catalog and theoretical predictions. The selection function defined over the observed quantities of flux and angular size is independent of cluster physics and cosmology, and thus provides a useful characterization of a survey. Selection expressed in terms of cluster mass and redshift, on the other hand, depends on both cosmology and cluster physics. We demonstrate that SZ catalogs are not simply flux limited, and illustrate how incorrect modeling of the selection function leads to biased estimates of cosmological parameters. The fact that SZ catalogs are not flux limited complicates survey ``calibration'' by requiring more detailed information on the relation between cluster observables and cluster mass.Comment: Accepted for publication in Astronomy & Astrophysics, 11 pages, 7 figure

Multiattribute preference models with reference points

In the context of multiple attribute decision making, preference models making use of reference points in an ordinal way have recently been introduced in the literature. This text proposes an axiomatic analysis of such models, with a particular emphasis on the case in which there is only one reference point. Our analysis uses a general conjoint measurement model resting on the study of traces induced on attributes by the preference relation and using conditions guaranteeing that these traces are complete. Models using reference points are shown to be a particular case of this general model. The number of reference points is linked to the number of equivalence classes distinguished by the traces. When there is only one reference point, the in- duced traces are quite rough, distinguishing at most two distinct equivalence classes. We study the relation between the model using a single reference point and other preference models proposed in the literature.

Statistical Characterization of Temperature Patterns in Anisotropic Cosmologies

We consider the issue of characterizing the coherent large-scale patterns from CMB temperature maps in globally anisotropic cosmologies. The methods we investigate are reasonably general; the particular models we test them on are the homogeneous but anisotropic relativistic cosmologies described by the Bianchi classification. Although the temperature variations produced in these models are not stochastic, they give rise to a "non-Gaussian" distribution of temperature fluctuations over the sky that is a partial diagnostic of the model. We explore two methods for quantifying non-Gaussian and/or non-stationary fluctuation fields in order to see how they respond to the Bianchi models.We first investigate the behavior of phase correlations between the spherical harmonic modes of the maps. Then we examine the behavior of the multipole vectors of the temperature distribution which, though defined in harmonic space, can indicate the presence of a preferred direction in real space, i.e. on the 2-sphere. These methods give extremely clear signals of the presence of anisotropy when applied to the models we discuss, suggesting that they have some promise as diagnostics of the presence of global asymmetry in the Universe.Comment: 14 pages, 10 figures, 4 tables, accepted by MNRA

Braids with as many full twists as strands realize the braid index

We characterize the fractional Dehn twist coefficient of a braid in terms of a slope of the homogenization of the Upsilon function, where Upsilon is the function-valued concordance homomorphism defined by Ozsv\'ath, Stipsicz, and Szab\'o. We use this characterization to prove that $n$-braids with fractional Dehn twist coefficient larger than $n-1$ realize the braid index of their closure. As a consequence, we are able to prove a conjecture of Malyutin and Netsvetaev stating that $n$-times twisted braids realize the braid index of their closure. We provide examples that address the optimality of our results. The paper ends with an appendix about the homogenization of knot concordance homomorphisms.Comment: 26 pages, 5 figures, comments welcome! V2: Implementation of referee suggestions. Accepted for publication by the Journal of Topolog