Supersymmetry, homology with twisted coefficients and n-dimensional knots

Let $n$ be any natural number. Let $K$ be any $n$-dimensional knot in $S^{n+2}$. We define a supersymmetric quantum system for $K$ with the following properties. We firstly construct a set of functional spaces (spaces of fermionic \{resp. bosonic\} states) and a set of operators (supersymmetric infinitesimal transformations) in an explicit way. Thus we obtain a set of the Witten indexes for $K$. Our Witten indexes are topological invariants for $n$-dimensional knots. Our Witten indexes are not zero in general. If $K$ is equivalent to the trivial knot, all of our Witten indexes are zero. Our Witten indexes restrict the Alexander polynomials of $n$-knots. If one of our Witten indexes for an $n$-knot $K$ is nonzero, then one of the Alexander polynomials of $K$ is nontrivial. Our Witten indexes are connected with homology with twisted coefficients. Roughly speaking, our Witten indexes have path integral representation by using a usual manner of supersymmetric theory.Comment: 10pages, no figure

The anomaly line bundle of the self-dual field theory

In this work, we determine explicitly the anomaly line bundle of the abelian self-dual field theory over the space of metrics modulo diffeomorphisms, including its torsion part. Inspired by the work of Belov and Moore, we propose a non-covariant action principle for a pair of Euclidean self-dual fields on a generic oriented Riemannian manifold. The corresponding path integral allows to study the global properties of the partition function over the space of metrics modulo diffeomorphisms. We show that the anomaly bundle for a pair of self-dual fields differs from the determinant bundle of the Dirac operator coupled to chiral spinors by a flat bundle that is not trivial if the underlying manifold has middle-degree cohomology, and whose holonomies are determined explicitly. We briefly sketch the relevance of this result for the computation of the global gravitational anomaly of the self-dual field theory, that will appear in another paper.Comment: 41 pages. v2: A few typos corrected. Version accepted for publication in CM

Compactification, topology change and surgery theory

We study the process of compactification as a topology change. It is shown how the mediating spacetime topology, or cobordism, may be simplified through surgery. Within the causal Lorentzian approach to quantum gravity, it is shown that any topology change in dimensions $\geq 5$ may be achieved via a causally continuous cobordism. This extends the known result for 4 dimensions. Therefore, there is no selection rule for compactification at the level of causal continuity. Theorems from surgery theory and handle theory are seen to be very relevant for understanding topology change in higher dimensions. Compactification via parallelisable cobordisms is particularly amenable to study with these tools.Comment: 1+19 pages. LaTeX. 9 associated eps files. Discussion of disconnected case adde

Cosmological Creation of D-branes and anti-D-branes

We argue that the early universe may be described by an initial state of space-filling branes and anti-branes. At high temperature this system is stable. At low temperature tachyons appear and lead to a phase transition, dynamics, and the creation of D-branes. These branes are cosmologically produced in a generic fashion by the Kibble mechanism. From an entropic point of view, the formation of lower dimensional branes is preferred and $D3$ brane-worlds are exponentially more likely to form than higher dimensional branes. Virtually any brane configuration can be created from such phase transitions by adjusting the tachyon profile. A lower bound on the number defects produced is: one D-brane per Hubble volume.Comment: 30 pages, 5 eps figures; v2 more references added; v3 section 4 slightly improve

DNA typing by microbead arrays and PCR-SSP: apparent false-negative or -positive hybridization or amplification signals disclose new HLA-B and -DRB1 alleles

Human leukocyte antigen (HLA) typing by polymerase chain reaction-sequence-specific oligonucleotide (PCR-SSO) hybridization on solid phase (microbead assay) or polymerase chain reaction-sequence-specific primers (PCR-SSP) requires interpretation softwares to detect all possible allele combinations. These programs propose allele calls by taking into account false-positive or false-negative signal(s). The laboratory has the option to validate typing results in the presence of strongly cross-reacting or apparent false-negative signals. Alternatively, these seemingly aberrant signals may disclose novel variants. We report here four new HLA-B (B*5620 and B*5716) and HLA-DRB1 alleles (DRB1*110107 and DRB1*1474) that were detected by apparent false-negative or -positive hybridization or amplification patterns, and ultimately resolved by sequencing. To avoid allele misassignments, a comprehensive evaluation of acquired data as documented in a quality assurance system is therefore required to confirm unambiguous typing interpretation

Sequence of a novel HLA-A2 allele in a haematopoietic stem cell donor of the international registry

We report here the sequence of a new human leucocyte antigen-A2 allele, A*9251, identified in a volunteer haematopoietic stem cell donor of the international registry. A*9251 differs from A*02010101 by two nucleotides at codons 113-114, resulting in a single His>Asp substitution at codon 114