Digital Repository

Links, Quantum Groups and TQFTs

Show simple item record

dc.contributor.advisor MISHRA, RAMA
dc.contributor.author BARAPATRE, SHRUTI
dc.date.accessioned 2024-05-20T04:00:31Z
dc.date.available 2024-05-20T04:00:31Z
dc.date.issued 2024-05
dc.identifier.citation 113 en_US
dc.identifier.uri http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/8856
dc.description.abstract This thesis aims to provide a detailed understanding of quantum invariants of knots and links. We present them as the link invariants derived from a representation of some quantum group. The most celebrated invariant, the Jones polynomial, is shown to be obtained from the fundamental representation of the quantum group Uh(sl2(C)), making it an example of a quantum invariant. In this thesis, we focus on the computation of the Jones polynomial. We provide a closed-form expression for the Jones polynomial of the weaving links W(3, m) and observe some patterns in the coefficients of the Jones polynomial of weaving links W(4, m). We emphasise the role of quantum groups as a general machinery for generating link invariants. It is known that for every semi-simple lie algebra g, one can obtain a quantum group Uh(g) and define a new link invariant for each of its representations. We also discuss a general approach for constructing link invariants called ‘Topological Quantum Field Theories (TQFTs)’. Quantum invariants are examples of 1-dimensional TQFTs. This thesis discusses the converse: every 1-dimensional TQFT arises from a representation of some quantum group. Looking at quantum invariants as 1-dimensional TQFTs allows us to generalise further and study invariants arising from n-dimensional TQFTs. Thus, one has a much broader definition of a quantum invariant, namely those arising from an n-dimensional TQFT. en_US
dc.description.sponsorship DST-INSPIRE SHE en_US
dc.language.iso en en_US
dc.subject Research Subject Categories::MATHEMATICS en_US
dc.title Links, Quantum Groups and TQFTs en_US
dc.type Thesis en_US
dc.description.embargo One Year en_US
dc.type.degree BS-MS en_US
dc.contributor.department Dept. of Mathematics en_US
dc.contributor.registration 20191165 en_US


Files in this item

This item appears in the following Collection(s)

  • MS THESES [1713]
    Thesis submitted to IISER Pune in partial fulfilment of the requirements for the BS-MS Dual Degree Programme/MSc. Programme/MS-Exit Programme

Show simple item record

Search Repository


Advanced Search

Browse

My Account