منابع مشابه
Quantum Invariant for Torus Link and Modular Forms
We consider an asymptotic expansion of Kashaev’s invariant or of the colored Jones function for the torus link T (2, 2m). We shall give q-series identity related to these invariants, and show that the invariant is regarded as a limit of q being N -th root of unity of the Eichler integral of a modular form of weight 3/2 which is related to the ŝu(2)m−2 character.
متن کاملQuantum Knot Invariant for Torus Link and Modular Forms
Recent studies reveal an intimate connection between the quantum knot invariant and the “nearly modular form” especially with the half integral weight. In Ref. 8 Lawrence and Zagier studied an asymptotic expansion of the Witten–Reshetikhin–Turaev invariant of the Poincaré homology sphere, and they showed that the invariant can be regarded as the Eichler integral of the modular form of weight 3/...
متن کاملHarmonic Maass Forms, Mock Modular Forms, and Quantum Modular Forms
This short course is an introduction to the theory of harmonic Maass forms, mock modular forms, and quantum modular forms. These objects have many applications: black holes, Donaldson invariants, partitions and q-series, modular forms, probability theory, singular moduli, Borcherds products, central values and derivatives of modular L-functions, generalized Gross-Zagier formulae, to name a few....
متن کاملOn iterated torus knots and transversal knots
A knot type is exchange reducible if an arbitrary closed n{braid representative K of K can be changed to a closed braid of minimum braid index nmin(K) by a nite sequence of braid isotopies, exchange moves and {destabilizations. (See Figure 1). In the manuscript [6] a transversal knot in the standard contact structure for S3 is de ned to be transversally simple if it is characterized up to trans...
متن کاملTransversal Torus Knots
We classify positive transversal torus knots in tight contact structures up to transversal isotopy.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Research in the Mathematical Sciences
سال: 2015
ISSN: 2197-9847
DOI: 10.1186/s40687-014-0016-3