Handel's fixed point theorem revisited

Michael Handel proved in [7] the existence of a fixed point for an orientation preserving homeomorphism of the open unit disk that can be extended to the closed disk, provided that it has points whose orbits form an oriented cycle of links at infinity. Later, Patrice Le Calvez gave a different proof of this theorem based only on Brouwer theory and plane topology arguments [9]. These methods permitted to improve the result by proving the existence of a simple closed curve of index 1. We give a new, simpler proof of this improved version of the theorem and generalize it to non-oriented cycles of links at infinityComment: Ergodic Theory and Dynamical Systems, Available on CJO 201

Manin's conjecture for a cubic surface with 2A_2+A_1 singularity type

We establish Manin's conjecture for a cubic surface split over Q and whose singularity type is 2A_2+A_1. For this, we make use of a deep result about the equidistribution of the values of a certain restricted divisor function in three variables in arithmetic progressions. This result is due to Friedlander and Iwaniec (and was later improved by Heath-Brown) and draws on the work of Deligne.Comment: 34 page

Water temperature dynamics in High Arctic river basins

Despite the high sensitivity of polar regions to climate change and the strong influence of temperature upon ecosystem processes, contemporary understanding of water temperature dynamics in Arctic river systems is limited. This research gap was addressed by exploring high-resolution water column thermal regimes for glacier-fed and non-glacial rivers at eight sites across Svalbard during the 2010 melt season. Mean water column temperatures in glacier-fed rivers (0.3-3.2 °C) were lowest and least variable near the glacier terminus but increased downstream (0.7-2.3 °C km ). Non-glacial rivers, where discharge was sourced primarily from snowmelt runoff, were warmer (mean: 2.9-5.7 °C) and more variable, indicating increased water residence times in shallow alluvial zones and increased potential for atmospheric influence. Mean summer water temperature and the magnitude of daily thermal variation were similar to those of some Alaskan Arctic rivers but low at all sites when compared with alpine glacierized environments at lower latitudes. Thermal regimes were correlated strongly (p<0.01) with incoming short-wave radiation, air temperature, and river discharge. Principal drivers of thermal variability were inferred to be (i) water source (i.e. glacier melt, snowmelt, groundwater); (ii) exposure time to the atmosphere; (iii) prevailing meteorological conditions; (iv) river discharge; (v) runoff interaction with permafrost and buried ice; and (vi) basin-specific geomorphological features (e.g. channel morphology). These results provide insight into the potential changes in high-latitude river systems in the context of projected warming in polar regions. We hypothesize that warmer and more variable temperature regimes may prevail in the future as the proportion of bulk discharge sourced from glacial meltwater declines and rivers undergo a progressive shift towards snow water and groundwater sources. Importantly, such changes could have implications for aquatic species diversity and abundance and influence rates of ecosystem functioning in high-latitude river systems

Evolution of a stream ecosystem in recently deglaciated terrain

Climate change and associated glacial recession create new stream habitat that leads to the assembly of new riverine communities through primary succession. However, there are still very few studies of the patterns and processes of community assembly during primary succession for stream ecosystems. We illustrate the rapidity with which biotic communities can colonize and establish in recently formed streams by examining Stonefly Creek in Glacier Bay, Alaska (USA), which began to emerge from a remnant glacial ice mass between 1976 and 1979. By 2002, 57 macroinvertebrate and 27 microcrustacea species had become established. Within 10 years of the stream's formation, pink salmon and Dolly Varden charr colonized, followed by other fish species, including juvenile red and silver salmon, Coast Range sculpin, and sticklebacks. Stable-isotope analyses indicate that marine-derived nitrogen from the decay of salmon carcasses was substantially assimilated within the aquatic food web by 2004. The findings from Stonefly Creek are compared with those from a long-term study of a similarly formed but older stream (12 km to the northeast) to examine possible similarities in macroinvertebrate community and biological trait composition between streams at similar stages of development. Macroinvertebrate community assembly appears to have been initially strongly deterministic owing to low water temperature associated with remnant ice masses. In contrast, microcrustacean community assembly appears to have been more stochastic. However, as stream age and water temperature increased, macroinvertebrate colonization was also more stochastic, and taxonomic similarity between Stonefly Creek and a stream at the same stage of development was,<50%. However the most abundant taxa were similar, and functional diversity of the two communities was almost identical. Tolerance is suggested as the major mechanism of community assembly. The rapidity with which salmonids and invertebrate communities have become established across an entire watershed has implications for the conservation of biodiversity in freshwater habitats

Homology cylinders and the acyclic closure of a free group

We give a Dehn-Nielsen type theorem for the homology cobordism group of homology cylinders by considering its action on the acyclic closure, which was defined by Levine, of a free group. Then we construct an additive invariant of those homology cylinders which act on the acyclic closure trivially. We also describe some tools to study the automorphism group of the acyclic closure of a free group generalizing those for the automorphism group of a free group or the homology cobordism group of homology cylinders.Comment: This is the version published by Algebraic & Geometric Topology on 7 April 200

Refined Kirby calculus for integral homology spheres

A theorem of Kirby states that two framed links in the 3-sphere produce orientation-preserving homeomorphic results of surgery if they are related by a sequence of stabilization and handle-slide moves. The purpose of the present paper is twofold: First, we give a sufficient condition for a sequence of handle-slides on framed links to be able to be replaced with a sequences of algebraically canceling pairs of handle-slides. Then, using the first result, we obtain a refinement of Kirby's calculus for integral homology spheres which involves only +/-1-framed links with zero linking numbers.Comment: This is the version published by Geometry & Topology on 18 September 200

Une nouvelle preuve du theoreme de point fixe de Handel

M Handel has proved in [Topology 38 (1999) 235--264] a fixed point theorem for an orientation preserving homeomorphism of the open unit disk, that may be extended to the closed disk and that satisfies a linking property of orbits. We give here a new proof of Handel's fixed point theorem, based on Brouwer theory and some plane topology arguments. We will slightly improve the theorem by proving the existence of a simple closed curve of index 1. This index result was known to be true under an additional hypothesis and has been used by different authors (J Franks [NYJM 2 (1996) 1--19, Trans.AMS 348 (1996) 2637--2662] S Matsumoto [Topol. Appl. 104 (2000) 191--214]) to study homeomorphisms of surfaces.Comment: This is the version published by Geometry & Topology on 8 December 200

A new look at C*-simplicity and the unique trace property of a group

We characterize when the reduced C*-algebra of a group has unique tracial state, respectively, is simple, in terms of Dixmier-type properties of the group C*-algebra. We also give a simple proof of the recent result by Breuillard, Kalantar, Kennedy and Ozawa that the reduced C*-algebra of a group has unique tracial state if and only if the amenable radical of the group is trivial.Comment: 8 page