Local homology and dimensional full-valuedness

A natural criterion for dimensional full-valuedness of locally compact spaces with finitely generated local homology is given.     

Noncommutative differential geometry on the quantum SU(2), I: An algebraic viewpoint

We compute the cyclic homology of the coordinate ring A(SL_q(2)) of the quantum algebraic group SL _q (2). We observe a degeneration of the noncommutative de Rham complex. The results are also verified from the point of view of Connes' noncommutative differential geometry.     

The search for a new model structure of β-Factor XIIa

We present the search for a new model of -factor XIIa, a blood coagulation enzyme, with an unknown experimental 3D-structure. We decided to build not one but three different models using different homologous proteins as well as different techniques and different modellers. Additional studies, including extensive molecular dynamics simulations on the solvated state, allowed us to draw several conclusions concerning homology modelling, in general, and -factor XIIa, in particular.     

Engineering cytochrome P-450s

Cytochrome P-450 isozymes represent a critical component of nature’s spectrum of detoxification catalysts that could be exploited for bioremediation. The ethanol-inducible human cytochrome P-450 2E1 serves as a model eukaryotic P-450 that complements the bacterial P-450 cam in dehalogenation and detoxification of environmental pollutants. We explored the construction of novel chimeric P-450s using cytochrome P-450 camC and 2E1 genes. For construction of chimera 1 (478 amino acids, 55.14 kDa), 145 amino acids from the N-terminus of P-450 2E1 protein (493 amino acids, 56.84 kDa) were replaced with 130 amino acids from the N-terminus of P-450 camC protein (415 amino acids, 46.66 kDa). In chimera 2 (525 amino acids, 60.24 kDa) the strategy involves replacement of 28 amino acids in the C-terminus of chimera 1 with 75 amino acids from the C-terminus of P-450 camC gene. Homology models of both the chimeric proteins were developed using SWISS-MODEL based on the known crystal structure of cytochrome P-450 camC, BM-3, 1DT6A, and 2C17A. The models indicated that the proposed heme-binding site was intact, which is inevitable for catalytic activity of cytochrome P-450s. The expression of chimera 1 and 2 genes in Escherichia coli DH5α was evident from light-pink cell pellets, protein band in sodium dodecyl sulfate polyacrylamide gel electrophoresis, and diagnostic carbon monoxide-difference spectra. Our studies show that strategies can be developed to exploit the natural diversity of the P-450 superfamily to generate chimeric biocatalysts that would provide new templates amenable to directed evolution.     

Homology and cohomology intersection numbers of GKZ systems

We describe the homology intersection form associated to regular holonomic GKZ systems in terms of the combinatorics of regular triangulations. Combining this result with the twisted period relation, we obtain a formula of cohomology intersection numbers in terms of a Laurent series. We show that the cohomology intersection number depends rationally on the parameters. We also prove a conjecture of F. Beukers and C. Verschoor on the signature of the monodromy invariant hermitian form.     

Complex homogeneous spaces of real groups with top homology in codimension two

SupposeX=G/H is a connected homogeneous complex manifold, whereG is a Lie group andH is a closed subgroup. Assume (X) and letG/H G/I be the holomorphic reduction ofX. If the top nonvanishing homology group ofX with coefficients in ₂ is in codimension two, then either a complex Lie group acts tansitively onG/I (see [3]) orG/I is biholomorphic to the unit disk.Partially supported by NSERC Grant A3494 and by the Deutsche Forschungsgemeinschaft     

Cyclic homology for schemes

Using hypercohomology, we can extend cyclic homology from algebras to all schemes over a ring . By `extend' we mean that the usual cyclic homology of any commutative algebra agrees with the cyclic homology of its corresponding affine scheme.

     

Geometric modules and Quinn homology theory

LetR be a ring with unit and invariant basis property. In [1], the authors define a functorK(_;R):TOP/LIP _c-LPEP by combining the open cone construction of [7] with a geometric module construction and show this functor is a homology theory. This paper shows that if attention is restricted to objects TOP/LIP _c with a homotopy colimit structure, then the functorK(_;R) is a Quinn homology theory, In particular, for each having a homotopy colimit structure,K(;R) is a homotopy colimit in the category of -spectra. Furthermore, the constituent spectra of this homotopy colimit are obtained naturally from the fibres of .Partially supported by the National Science Foundation under grant number DMS88-03148.Partially supported by the SNF (Denmark) under grant number 11-7792.     

NonstableK-Theory for operator algebras

We show that the homotopy groups of the group of quasi-unitaries inC ^*-algebras form a homology theory on the category of allC ^*-algebras which becomes topologicalK-theory when stabilized. We then show how this functorial setting, in particular the half-exactness of the involved functors, helps to calculate the homotopy groups of the group of unitaries in a series ofC ^*-algebras. The calculations include the case of all AbelianC ^*-algebras and allC ^*-algebras of the formAB, whereA is one of the Cuntz algebras O_n n=2, 3, ..., an infinite dimensional simpleAF-algebra, the stable multiplier or corona algebra of a-unitalC ^*-algebra, a properly infinite von Neumann algebra, or one of the projectionless simpleC ^*-algebras constructed by Blackadar.     

On the minimal sum of Betti numbers of an almost complex manifold

We show that the only rational homology spheres which can admit almost complex structures occur in dimensions two and six. Moreover, we provide infinitely many examples of six-dimensional rational homology spheres which admit almost complex structures, and infinitely many which do not. We then show that if a closed almost complex manifold has sum of Betti numbers three, then its dimension must be a power of two.