297 research outputs found
Equivariant geometric K-homology for compact Lie group actions
Let G be a compact Lie-group, X a compact G-CW-complex. We define equivariant
geometric K-homology groups K^G_*(X), using an obvious equivariant version of
the (M,E,f)-picture of Baum-Douglas for K-homology. We define explicit natural
transformations to and from equivariant K-homology defined via KK-theory (the
"official" equivariant K-homology groups) and show that these are isomorphism.Comment: 25 pages. v2: some mistakes corrected, more detail added, Michael
Walter as author added. To appear in Abhandlungen aus dem Mathematischen
Seminar der Universit\"at Hambur
Differential sensitivity of brainstem vs cortical astrocytes to changes in pH reveals functional regional specialization of astroglia
Astrocytes might function as brain interoceptors capable of detecting different (chemo)sensory modalities and transmitting sensory information to the relevant neural networks controlling vital functions. For example, astrocytes which reside near the ventral surface of the brainstem (central respiratory chemosensitive area) respond to physiological decreases in pH with vigorous elevations in intracellular Ca(2+) and release of ATP. ATP transmits astroglial excitation to the brainstem respiratory network and contributes to adaptive changes in lung ventilation. Here we show that in terms of pH-sensitivity ventral brainstem astrocytes are clearly distinct from astrocytes residing in the cerebral cortex. We monitored vesicular fusion in cultured rat brainstem astrocytes using total internal reflection fluorescence microscopy and found that approximately 35% of them respond to acidification with an increased rate of exocytosis of ATP-containing vesicular compartments. These fusion events require intracellular Ca(2+) signaling and are independent of autocrine ATP actions. In contrast, the rate of vesicular fusion in cultured cortical astrocytes is not affected by changes in pH. Compared to cortical astrocytes, ventral brainstem astrocytes display higher levels of expression of genes encoding proteins associated with ATP vesicular transport and fusion, including vesicle-associated membrane protein-3 and vesicular nucleotide transporter. These results suggest that astrocytes residing in different parts of the rat brain are functionally specialized. In contrast to cortical astrocytes, astrocytes of the brainstem chemosensitive area(s) possess signaling properties which are functionally relevant – they are able to sense changes in pH and respond to acidification with enhanced vesicular release of ATP
Equivariant Lefschetz maps for simplicial complexes and smooth manifolds
Let X be a locally compact space with a continuous proper action of a locally
compact group G. Assuming that X satisfies a certain kind of duality in
equivariant bivariant Kasparov theory, we can enrich the classical construction
of Lefschetz numbers to equivariant K-homology classes. We compute the
Lefschetz invariants for self-maps of finite-dimensional simplicial complexes
and of self-maps of smooth manifolds. The resulting invariants are independent
of the extra structure used to compute them. Since smooth manifolds can be
triangulated, we get two formulas for the same Lefschetz invariant in these
cases. The resulting identity is closely related to the equivariant Lefschetz
Fixed Point Theorem of Luck and Rosenberg.Comment: Minor revisions, affecting some theorem number
Operator *-correspondences in analysis and geometry
An operator *-algebra is a non-selfadjoint operator algebra with completely
isometric involution. We show that any operator *-algebra admits a faithful
representation on a Hilbert space in such a way that the involution coincides
with the operator adjoint up to conjugation by a symmetry. We introduce
operator *-correspondences as a general class of inner product modules over
operator *-algebras and prove a similar representation theorem for them. From
this we derive the existence of linking operator *-algebras for operator
*-correspondences. We illustrate the relevance of this class of inner product
modules by providing numerous examples arising from noncommutative geometry.Comment: 31 pages. This work originated from the MFO workshop "Operator spaces
and noncommutative geometry in interaction
Expression of Microbial Enzymes in Mammalian Astrocytes to Modulate Lactate Release
Astrocytes support and modulate neuronal activity through the release of L-lactate. The
suggested roles of astrocytic lactate in the brain encompass an expanding range of vital functions,
including central control of respiration and cardiovascular performance, learning, memory, executive
behaviour and regulation of mood. Studying the effects of astrocytic lactate requires tools that limit
the release of lactate selectively from astrocytes. Here, we report the validation in vitro of novel
molecular constructs derived from enzymes originally found in bacteria, that when expressed in
astrocytes, interfere with lactate handling. When lactate 2-monooxygenase derived from M. smegmatis
was specifically expressed in astrocytes, it reduced intracellular lactate pools as well as lactate release
upon stimulation. D-lactate dehydrogenase derived from L. bulgaricus diverts pyruvate towards
D-lactate production and release by astrocytes, which may affect signalling properties of lactate in
the brain. Together with lactate oxidase, which we have previously described, this set of transgenic
tools can be employed to better understand astrocytic lactate release and its role in the regulation of
neuronal activity in different behavioural contexts
The Baum-Connes Conjecture via Localisation of Categories
We redefine the Baum-Connes assembly map using simplicial approximation in
the equivariant Kasparov category. This new interpretation is ideal for
studying functorial properties and gives analogues of the assembly maps for all
equivariant homology theories, not just for the K-theory of the crossed
product. We extend many of the known techniques for proving the Baum-Connes
conjecture to this more general setting
Uniformization and an Index Theorem for Elliptic Operators Associated with Diffeomorphisms of a Manifold
We consider the index problem for a wide class of nonlocal elliptic operators
on a smooth closed manifold, namely differential operators with shifts induced
by the action of an isometric diffeomorphism. The key to the solution is the
method of uniformization: We assign to the nonlocal problem a
pseudodifferential operator with the same index, acting in sections of an
infinite-dimensional vector bundle on a compact manifold. We then determine the
index in terms of topological invariants of the symbol, using the Atiyah-Singer
index theorem.Comment: 16 pages, no figure
Homology and K--Theory Methods for Classes of Branes Wrapping Nontrivial Cycles
We apply some methods of homology and K-theory to special classes of branes
wrapping homologically nontrivial cycles. We treat the classification of
four-geometries in terms of compact stabilizers (by analogy with Thurston's
classification of three-geometries) and derive the K-amenability of Lie groups
associated with locally symmetric spaces listed in this case. More complicated
examples of T-duality and topology change from fluxes are also considered. We
analyse D-branes and fluxes in type II string theory on with torsion flux and demonstrate in details
the conjectured T-duality to with no flux. In the
simple case of , T-dualizing the circles reduces to
duality between with
flux and with no flux.Comment: 27 pages, tex file, no figure
Horses for the dead: funerary foodways in Bronze Age Kazakhstan
© 2011 Antiquity PublicationsThe authors examine the role of horses as expressed in assemblages from settlement sites and cemeteries between the Eneolithic and the Bronze Age in Kazakhstan. In this land, known for its rich association with horses, the skeletal evidence appears to indicate a fading of ritual interest. But that's not the whole story, and once again micro-archaeology reveals the true balance. The horses are present at the funeral, but now as meat for the pot, detected in bone fragments and lipids in the pot walls.Natural Environment Research Council
(grant NE/B504506) and the British Academy (grants SG-35540 and SG-42656)
Equivariant comparison of quantum homogeneous spaces
We prove the deformation invariance of the quantum homogeneous spaces of the
q-deformation of simply connected simple compact Lie groups over the
Poisson-Lie quantum subgroups, in the equivariant KK-theory with respect to the
translation action by maximal tori. This extends a result of Neshveyev-Tuset to
the equivariant setting. As applications, we prove the ring isomorphism of the
K-group of Gq with respect to the coproduct of C(Gq), and an analogue of the
Borsuk-Ulam theorem for quantum spheres.Comment: 21 page
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