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11
Black Hole Entropy, Topological Entropy and Noncommutative Geometry
, 2001
"... izois @ maths.ox.ac.uk; Research supported by the EU, contract no HPMF ..."
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izois @ maths.ox.ac.uk; Research supported by the EU, contract no HPMF
The GodbillonVey class, invariants of manifolds and linearised MTheory
"... izois @ maths.ox.ac.uk and izois @ cc.uoa.gr; Research supported by the EU, ..."
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izois @ maths.ox.ac.uk and izois @ cc.uoa.gr; Research supported by the EU,
Multiple ”parallel” Dbranes seen as leaves of foliations and Duminy’s theorem” hepth/0011228. ” On search for the MTheory Lagrangian” hepth/9703067. ”Foliations with nonvanishing GVclass and gauge invariance” hepth/0303158. ”GelfandFuchs cohomology
"... izois @ maths.ox.ac.uk; Research supported by the EU, contract no HPMF ..."
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izois @ maths.ox.ac.uk; Research supported by the EU, contract no HPMF
Noncommutativity vs gauge symmetry
, 2005
"... In many aspects the most complicated foliated manifolds are those with nonvanishing GodbillonVey class. We argue that they probably do not appear in physics and that is due to gauge symmetry which prevents the foliation from becoming “too wild”; that means that the foliation does not develop resili ..."
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In many aspects the most complicated foliated manifolds are those with nonvanishing GodbillonVey class. We argue that they probably do not appear in physics and that is due to gauge symmetry which prevents the foliation from becoming “too wild”; that means that the foliation does not develop resilient leaves which, at least in codim1, by Duminy’s theorem are responsible for the nontriviality of the GVclass. PACS classification: 11.10.z; 11.15.q; 11.30.Ly Keywords: GodbillonVey class, foliations, noncommutative geometry, supergravity, MTheory
An application of the GodbillonVey class in MTheory
, 2000
"... We apply the GodbillonVey class to compute the transition amplitudes between some noncommutative solitons in MTheory; our context is that of ConnesDouglasSchwarz where they considered compactifications of matrix models on noncommutative tori. Moreover we try to clarify the topological Lagrangia ..."
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We apply the GodbillonVey class to compute the transition amplitudes between some noncommutative solitons in MTheory; our context is that of ConnesDouglasSchwarz where they considered compactifications of matrix models on noncommutative tori. Moreover we try to clarify the topological Lagrangian density suggested for MTheory in a previous article using the fact that the functor of immersions is a linearisation of the functor of embeddings. PACS classification: 11.10.z; 11.15.q; 11.30.Ly Keywords: GodbillonVey class, MTheory, KTheory, solitons0.1 Some remarks on KTheories... Let M be a closed smooth nmanifold. A codimension q foliation where 0 < q < n, is a particular example of a Haefliger or Γqstructure on M. A codimq foliation is defined by specifying a codimq integrable subbundle F of the tangent bundle TM of M. A local definition is provided by specifying a nowhere vanishing decomposable qform Ω on M. The integrability condition is expressed by the relation
Noncommutative Topological Quantum Field
, 2005
"... We present some ideas for a possible Noncommutative Floer Homology. The geometric motivation comes from an attempt to build a theory which applies to practically every 3manifold (closed, oriented and connected) and not only to homology 3spheres. There is also a physical motivation: one would like ..."
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We present some ideas for a possible Noncommutative Floer Homology. The geometric motivation comes from an attempt to build a theory which applies to practically every 3manifold (closed, oriented and connected) and not only to homology 3spheres. There is also a physical motivation: one would like to construct a noncommutative topological quantum field theory. The two motivations are closely related since in the commutative case at least, Floer Homology Groups are part of a certain (3+1)dim Topological Quantum Field Theory. Classification: theoretical physics, mathematical physics, geometric topology, differential geometry, quantum algebra
Foliations with nonvanishing GVclass and gauge invariance
, 2003
"... In many aspects the most complicated foliated manifolds are those with nonvanishing GodbillonVey class. We argue that they probably do not appear in physics and that is due to gauge symmetry which prevents the foliation from becoming “too wild”; that means that the foliation does not develop resili ..."
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In many aspects the most complicated foliated manifolds are those with nonvanishing GodbillonVey class. We argue that they probably do not appear in physics and that is due to gauge symmetry which prevents the foliation from becoming “too wild”; that means that the foliation does not develop resilient leaves which, at least in codim1, by Duminy’s theorem are responsible for the appearence of nontrivial
The Mobius Band and the Mobius Foliation
, 2008
"... Some years ago we introduced a new topological invariant for foliated manifolds using techniques from noncommutative geometry, in particular the pairing between KTheory and cyclic cohomology. The motivation came from flat principal Gbundles where the base space is a non simply connected manifold. ..."
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Some years ago we introduced a new topological invariant for foliated manifolds using techniques from noncommutative geometry, in particular the pairing between KTheory and cyclic cohomology. The motivation came from flat principal Gbundles where the base space is a non simply connected manifold. The computation of this invariant is quite complicated. In this article we try to perform certain computations for the Mobius band (or Mobius foliation) which is an interesting nontrivial example of foliations; this example has a key feature: it is the simplest case of a large class of examples of foliations, that of bundles with discrete structure groups which also includes the foliations given by flat vector (or Gprincipal) bundles. We shall see that the Mobius foliation example also helps one to understand another large class of examples of foliations coming from group actions on manifolds which are not free.