29 research outputs found
A unified Witten-Reshetikhin-Turaev invariant for integral homology spheres
We construct an invariant J_M of integral homology spheres M with values in a
completion \hat{Z[q]} of the polynomial ring Z[q] such that the evaluation at
each root of unity \zeta gives the the SU(2) Witten-Reshetikhin-Turaev
invariant \tau_\zeta(M) of M at \zeta. Thus J_M unifies all the SU(2)
Witten-Reshetikhin-Turaev invariants of M. As a consequence, \tau_\zeta(M) is
an algebraic integer. Moreover, it follows that \tau_\zeta(M) as a function on
\zeta behaves like an ``analytic function'' defined on the set of roots of
unity. That is, the \tau_\zeta(M) for all roots of unity are determined by a
"Taylor expansion" at any root of unity, and also by the values at infinitely
many roots of unity of prime power orders. In particular, \tau_\zeta(M) for all
roots of unity are determined by the Ohtsuki series, which can be regarded as
the Taylor expansion at q=1.Comment: 66 pages, 8 figure
A TQFT associated to the LMO invariant of three-dimensional manifolds
We construct a Topological Quantum Field Theory (in the sense of Atiyah)
associated to the universal finite-type invariant of 3-dimensional manifolds,
as a functor from the category of 3-dimensional manifolds with parametrized
boundary, satisfying some additional conditions, to an algebraic-combinatorial
category. It is built together with its truncations with respect to a natural
grading, and we prove that these TQFTs are non-degenerate and anomaly-free. The
TQFT(s) induce(s) a (series of) representation(s) of a subgroup of
the Mapping Class Group that contains the Torelli group. The N=1 truncation
produces a TQFT for the Casson-Walker-Lescop invariant.Comment: 28 pages, 13 postscript figures. Version 2 (Section 1 has been
considerably shorten, and section 3 has been slightly shorten, since they
will constitute a separate paper. Section 4, which contained only announce of
results, has been suprimated; it will appear in detail elsewhere.
Consequently some statements have been re-numbered. No mathematical changes
have been made.
Super-A-polynomials for Twist Knots
We conjecture formulae of the colored superpolynomials for a class of twist
knots where p denotes the number of full twists. The validity of the
formulae is checked by applying differentials and taking special limits. Using
the formulae, we compute both the classical and quantum super-A-polynomial for
the twist knots with small values of p. The results support the categorified
versions of the generalized volume conjecture and the quantum volume
conjecture. Furthermore, we obtain the evidence that the Q-deformed
A-polynomials can be identified with the augmentation polynomials of knot
contact homology in the case of the twist knots.Comment: 22+16 pages, 16 tables and 5 figures; with a Maple program by Xinyu
Sun and a Mathematica notebook in the ancillary files linked on the right; v2
change in appendix B, typos corrected and references added; v3 change in
section 3.3; v4 corrections in Ooguri-Vafa polynomials and quantum
super-A-polynomials for 7_2 and 8_1 are adde
The Pure Virtual Braid Group Is Quadratic
If an augmented algebra K over Q is filtered by powers of its augmentation
ideal I, the associated graded algebra grK need not in general be quadratic:
although it is generated in degree 1, its relations may not be generated by
homogeneous relations of degree 2. In this paper we give a sufficient criterion
(called the PVH Criterion) for grK to be quadratic. When K is the group algebra
of a group G, quadraticity is known to be equivalent to the existence of a (not
necessarily homomorphic) universal finite type invariant for G. Thus the PVH
Criterion also implies the existence of such a universal finite type invariant
for the group G. We apply the PVH Criterion to the group algebra of the pure
virtual braid group (also known as the quasi-triangular group), and show that
the corresponding associated graded algebra is quadratic, and hence that these
groups have a (not necessarily homomorphic) universal finite type invariant.Comment: 53 pages, 15 figures. Some clarifications added and inaccuracies
corrected, reflecting suggestions made by the referee of the published
version of the pape
String theory and the Kauffman polynomial
We propose a new, precise integrality conjecture for the colored Kauffman
polynomial of knots and links inspired by large N dualities and the structure
of topological string theory on orientifolds. According to this conjecture, the
natural knot invariant in an unoriented theory involves both the colored
Kauffman polynomial and the colored HOMFLY polynomial for composite
representations, i.e. it involves the full HOMFLY skein of the annulus. The
conjecture sheds new light on the relationship between the Kauffman and the
HOMFLY polynomials, and it implies for example Rudolph's theorem. We provide
various non-trivial tests of the conjecture and we sketch the string theory
arguments that lead to it.Comment: 36 pages, many figures; references and examples added, typos
corrected, final version to appear in CM
Complementary effects of HDAC inhibitor 4-PB on gap junction communication and cellular export mechanisms support restoration of chemosensitivity of PDAC cells
Pancreatic ductal adenocarcinoma (PDAC) is a fatal disease and one of the cancer entities with the lowest life expectancy. Beside surgical therapy, no effective therapeutic options are available yet. Here, we show that 4-phenylbutyrate (4-PB), a known and well-tolerable inhibitor of histone deacetylases (HDAC), induces up to 70% apoptosis in all cell lines tested (Panc 1, T4M-4, COLO 357, BxPc3). In contrast, it leads to cell cycle arrest in only half of the cell lines tested. This drug increases gap junction communication between adjacent T3M-4 cells in a concentration-dependent manner and efficiently inhibits cellular export mechanisms in Panc 1, T4M-4, COLO 357 and BxPc3 cells. Consequently, in combination with gemcitabine 4-PB shows an overadditive effect on induction of apoptosis in BxPc3 and T3M-4 cells (up to 4.5-fold compared to single drug treatment) with accompanied activation of Caspase 8, BH3 interacting domain death agonist (Bid) and poly (ADP-ribose) polymerase family, member 1 (PARP) cleavage. Although the inhibition of the mitogen-activated protein kinase-pathway has no influence on fulminant induction of apoptosis, the inhibition of the JNK-pathway by SP600125 completely abolishes the overadditive effect induced by the combined application of both drugs, firstly reported by this study
Holomorphic Blocks in Three Dimensions
We decompose sphere partition functions and indices of three-dimensional N=2
gauge theories into a sum of products involving a universal set of "holomorphic
blocks". The blocks count BPS states and are in one-to-one correspondence with
the theory's massive vacua. We also propose a new, effective technique for
calculating the holomorphic blocks, inspired by a reduction to supersymmetric
quantum mechanics. The blocks turn out to possess a wealth of surprising
properties, such as a Stokes phenomenon that integrates nicely with actions of
three-dimensional mirror symmetry. The blocks also have interesting dual
interpretations. For theories arising from the compactification of the
six-dimensional (2,0) theory on a three-manifold M, the blocks belong to a
basis of wavefunctions in analytically continued Chern-Simons theory on M. For
theories engineered on branes in Calabi-Yau geometries, the blocks offer a
non-perturbative perspective on open topological string partition functions.Comment: 124 pages, 21 figures. v3: Typos correcte