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

Non-isotopic Heegaard splittings of Seifert fibered spaces

We find a geometric invariant of isotopy classes of strongly irreducible Heegaard splittings of toroidal 3-manifolds. Combining this invariant with a theorem of R Weidmann, proved here in the appendix, we show that a closed, totally orientable Seifert fibered space M has infinitely many isotopy classes of Heegaard splittings of the same genus if and only if M has an irreducible, horizontal Heegaard splitting, has a base orbifold of positive genus, and is not a circle bundle. This characterizes precisely which Seifert fibered spaces satisfy the converse of Waldhausen's conjecture.Comment: This is the version published by Algebraic & Geometric Topology on 12 March 200

Giving meaning to identities. A case-study for the Romanian Banat region

This research is focussed on the ethnic identities from Banat maintained till nowadays under different cultural forms. Identity starts from the feeling of ‘social space’, with a specific language for each ethnic group and a specific culture evolving through time. These local ethnic identities have determined the appearance of a regional identity. A questionnaire was launched among over 500 students and many interviews were conducted, reaching the conclusion that the spirit of ‘banaţean’native of Banat) is still alive among young people, albeit with a lower. Politically, local actors participate in projects to maintain regional identity, while at the central government level seem to embrace the Banat cultural identity.ethnic and regional identity, cultural symbols, Banat, Romania

The minimal volume orientable hyperbolic 3-manifold with 4 cusps

We prove that the 8^4_2 link complement is the minimal volume orientable hyperbolic manifold with 4 cusps. Its volume is twice of the volume V_8 of the ideal regular octahedron, i.e. 7.32... = 2V_8. The proof relies on Agol's argument used to determine the minimal volume hyperbolic 3-manifolds with 2 cusps. We also need to estimate the volume of a hyperbolic 3-manifold with totally geodesic boundary which contains an essential surface with non-separating boundary.Comment: 22 pages, 16 figure

A Typical Verification Challenge for the GRID

A typical verification challenge for the GRID community is\ud presented. The concrete challenge is to implement a simple recursive algorithm for finding the strongly connected components in a graph. The graph is typically stored in the collective memory of a number of computers, so a distributed algorithm is necessary.\ud \ud The implementation should be efficient and scalable, and separate synchronization and implementation details from the purely algorithmic aspects. In the end, a framework is envisaged for distributed algorithms on very large graphs. This would be useful to explore various alternative algorithmic choices

Atmospheric hypoxia limits selection for large body size in insects

Recent geological models indicate a marked increase in atmospheric oxygen partial pressure (aPO~2~) to 32 kPa in the Permo-Carboniferous (approx. 300 million years ago), subsequently falling to 13 kPa in the Triassic^1^.These aPO~2~ changes have been hypothesized to cause multiple major evolutionary events^2^ including the appearance and subsequent extinction of giant insects and other taxa^3, 4^. Patterns of increasing tracheal investment in larger insects support this hypothesis^5^, as do observations of positive relationships between aPO~2~ and body size in single- or multi-generational experiments with _Drosophila melanogaster_ and other insects^6^. Large species likely result from many generations of selection for large body size driven by predation, competition or sexual selection^7^. Thus a crucial question is whether aPO~2~ influences the capacity of such selection to increase insect size. We tested that possibility by selecting for large body size in five _Drosophila melanogaster_ populations for 11 generations in hypoxic (10 kPa), normoxic (21 kPa) and hyperoxic (40 kPa) aPO~2~, followed by three generations of normoxia without size selection to test for evolved responses. Average body sizes increased by 15% during 11 generations of size selection in 21 and 40 kPa aPO~2~ flies and even stronger responses were observed for the flies in the largest quartile of body masses. However, flies selected for large size in 10 kPa aPO~2~ had strongly reduced sizes compared to those in higher aPO~2~. Upon return to normoxia, all flies had similar, enlarged sizes relative to the starting populations. These results demonstrated that positive size selection had equivalent genetic effects on all flies independent of aPO~2~, but that hypoxia provided a physical constraint on body size even in a relatively small insect under strong selection for larger mass. Our data support the hypothesis that Triassic hypoxia may have contributed to a reduction in insect size

Canonical decompositions of 3-manifolds

We describe a new approach to the canonical decompositions of 3-manifolds along tori and annuli due to Jaco-Shalen and Johannson (with ideas from Waldhausen) - the so-called JSJ-decomposition theorem. This approach gives an accessible proof of the decomposition theorem; in particular it does not use the annulus-torus theorems, and the theory of Seifert fibrations does not need to be developed in advance.Comment: 20 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol1/paper3.abs.htm