000			02002nam a2200265Ia 4500
003			OSt
005			20250724142316.0
008			220909b |||||||| |||| 00| 0 eng d
020			_a9789814520591
037			_cTextbook
040			_aCSL _beng _cCSL
041			_aeng
084			_aB397 Q4;1 TB _qCSL
100			_aGelca, Razvan _eauthor _9462495
245		0	_aTheta functions and knots
260			_aSingapore : _bWSP, _c2014.
300			_axiv, 454p. _b: ill.
500			_aBibliography 445-450p.; Index 451-454p.
520			_aThis book presents the relationship between classical theta functions and knots. It is based on a novel idea of Răzvan Gelca and Alejandro Uribe, which converts Weil's representation of the Heisenberg group on theta functions to a knot theoretical framework, by giving a topological interpretation to a certain induced representation. It also explains how the discrete Fourier transform can be related to 3- and 4-dimensional topology.Theta Functions and Knots can be read in two perspectives. Readers with an interest in theta functions or knot theory can learn how the two are related. Those interested in Chern-Simons theory will find here an introduction using the simplest case, that of abelian Chern-Simons theory. Moreover, the construction of abelian Chern-Simons theory is based entirely on quantum mechanics and not on quantum field theory as it is usually done. Both the theory of theta functions and low dimensional topology are presented in detail, in order to underline how deep the connection between these two fundamental mathematical subjects is. Hence the book is self-contained with a unified presentation. It is suitable for an advanced graduate course, as well as for self-study.
650			_a Prototype _9816406
650			_a Surfaces _9816407
650			_aTopological quantum _9816408
942			_hB397 Q4;1 TB _cTB _2CC _n0
999			_c15935 _d15935