thesis.bib

@article{ivanov_connected_2021,
	title = {Connected sum of virtual knots and {F}-polynomials},
	volume = {30},
	issn = {0218-2165},
	url = {https://worldscientific-com.myaccess.library.utoronto.ca/doi/10.1142/S0218216521400022},
	doi = {10.1142/S0218216521400022},
	abstract = {It is known that connected sum of two virtual knots is not uniquely determined and depends on knot diagrams and choosing the points to be connected. But different connected sums of the same virtual knots cannot be distinguished by Kauffman’s affine index polynomial. For any pair of virtual knots K and M with n-dwrithe ∇Jn(K)≠0 we construct an infinite family of different connected sums of K and M which can be distinguished by F-polynomials.},
	pages = {2140002},
	number = {10},
	journaltitle = {Journal of Knot Theory and Its Ramifications},
	shortjournal = {J. Knot Theory Ramifications},
	author = {Ivanov, Maxim},
	urldate = {2022-09-15},
	date = {2021-09},
	publisher = {World Scientific Publishing Co.},
	keywords = {connected sum, F-polynomial, Virtual knot},
	file = {Full Text PDF:/home/jesse/Zotero/storage/UR9BUVJF/Ivanov - 2021 - Connected sum of virtual knots and F-polynomials.pdf:application/pdf},
}

@article{BV,
	Title = {Perturbed {Gaußian} Generating Functions for Universal Knot Invariants},
	url = {http://arxiv.org/abs/2109.02057},
	doi = {10.48550/arXiv.2109.02057},
	number = {{arXiv}:2109.02057},
	publisher = {{arXiv}},
	author = {Bar-Natan, Dror and van der Veen, Roland},
	urldate = {2022-10-05},
	date = {2021-09-05},
	eprinttype = {arxiv},
	eprint = {2109.02057 [math]},
	keywords = {57M25, Mathematics - Geometric Topology, Mathematics - Quantum Algebra},
	file = {arXiv Fulltext PDF:/home/jesse/Zotero/storage/DX9LS2KC/Bar-Natan and van der Veen - 2021 - Perturbed Gaussian generating functions for univer.pdf:application/pdf;arXiv.org Snapshot:/home/jesse/Zotero/storage/PCPVGFM9/2109.html:text/html},
}

@book{ES,
	title = {Lectures on Quantum Groups},
	isbn = {978-1-57146-063-9},
	abstract = {Based on lectures given in the spring of 1997 at Harvard University, this book is an introduction to the theory of quantum groups and its development between 1982 and 1997. Topics covered include: relevant quasiclassical objects; bialgebras; Hopf algebras; and lie associators.},
	pagetotal = {264},
	publisher = {International Press},
	author = {Etingof, Pavel I. and Schiffmann, Olivier},
	date = {1998},
	langid = {english},
}
@book{SM,
        location = {Cambridge},
        title = {A Quantum Groups Primer},
        isbn = {978-0-521-01041-2},
        url = {https://www.cambridge.org/core/books/quantum-groups-primer/9B4F8F074F6E060E63F87E665365E89E},
        series = {London Mathematical Society Lecture Note Series},
        abstract = {This book provides a self-contained introduction to quantum groups as algebraic objects. Based on the author's lecture notes from a Part {III} pure mathematics course at Cambridge University, it is suitable for use as a textbook for graduate courses in quantum groups or as a supplement to modern courses in advanced algebra. The book assumes a background knowledge of basic algebra and linear algebra. Some familiarity with semisimple Lie algebras would also be helpful. The book is aimed as a primer for mathematicians and takes a modern approach leading into knot theory, braided categories and noncommutative differential geometry. It should also be useful for mathematical physicists.},
        publisher = {Cambridge University Press},
        author = {Majid, Shahn},
        urldate = {2023-01-23},
        date = {2002},
        doi = {10.1017/CBO9780511549892},
        file = {Snapshot:/home/jesse/Zotero/storage/EYGLILPT/9B4F8F074F6E060E63F87E665365E89E.html:text/html},
}
@article{BS,
  title = {Meta-monoids, meta-bicrossed products, and the {Alexander} polynomial},
  volume = {22},
  issn = {0218-2165},
  url = {https://www.worldscientific.com/doi/abs/10.1142/S0218216513500582},
  doi = {10.1142/S0218216513500582},
  abstract = {We introduce a new invariant of tangles along with an algebraic framework in which it is to be interpreted. We claim that the invariant contains the classical Alexander polynomial of knots and its multivariable extension to links. We argue that of the computationally efficient members of the family of Alexander invariants, it is the most meaningful.

These are lecture notes for talks given by the first author, written and completed by the second. The talks, with handouts and videos, are available at http://www.math.toronto.edu/drorbn/Talks/Regina-1206/. See also further comments at http://www.math.toronto.edu/drorbn/Talks/Caen-1206/\#June8.},
  pages = {1350058},
  number = {10},
  journaltitle = {Journal of Knot Theory and Its Ramifications},
  shortjournal = {J. Knot Theory Ramifications},
  author = {Bar-Natan, Dror and Selmani, Sam},
  urldate = {2023-06-06},
  date = {2013-09},
  note = {Publisher: World Scientific Publishing Co.},
  keywords = {Alexander polynomial, bicrossed products, meta-groups, Meta-monoids},
  file = {Full Text PDF:/home/jesse/Zotero/storage/9SMCNCHZ/Bar-Natan and Selmani - 2013 - Meta-monoids, meta-bicrossed products, and the ale.pdf:application/pdf},
}

@article{BV23,
        title = {A Perturbed-{Alexander} Invariant},
        url = {http://arxiv.org/abs/2206.12298},
        doi = {10.48550/arXiv.2206.12298},
        number = {{arXiv}:2206.12298},
        publisher = {{arXiv}},
        author = {Bar-Natan, Dror and van der Veen, Roland},
        urldate = {2023-06-09},
        date = {2022-06-27},
        eprinttype = {arxiv},
        eprint = {2206.12298 [math]},
        keywords = {57K14, 16T99, Mathematics - Geometric Topology, Mathematics - Quantum Algebra},
        file = {arXiv Fulltext PDF:/home/jesse/Zotero/storage/LRJ6WHGI/Bar-Natan and van der Veen - 2022 - A Perturbed-Alexander Invariant.pdf:application/pdf;arXiv.org Snapshot:/home/jesse/Zotero/storage/BHLDCWK9/2206.html:text/html},
}

@article{LK,
	title = {Rotational Virtual Knots and Quantum Link Invariants},
	url = {https://www.worldscientific.com/doi/epdf/10.1142/S0218216515410084},
	doi = {10.1142/S0218216515410084},
	abstract = {This paper studies rotational virtual knot theory and its relationship with quantum link invariants. Every quantum link invariant for classical knots and links extends to an invariant of rotational...},
	journaltitle = {Journal of Knot Theory and Its Ramifications},
	author = {Kauffman, Louis H.},
	urldate = {2023-07-20},
	date = {2015-12-16},
	langid = {english},
	publisher = {World Scientific Publishing Company},
	file = {Snapshot:/home/jesse/Zotero/storage/QMAV4PKZ/S0218216515410084.html:text/html;Submitted Version:/home/jesse/Zotero/storage/U78NNQ8K/Kauffman - 2015 - Rotational virtual knots and quantum link invarian.pdf:application/pdf},
}

@book{lickorish,
	title = {An Introduction to Knot Theory},
	isbn = {978-1-4612-0691-0},
	pagetotal = {213},
	publisher = {Springer Science \& Business Media},
	author = {Lickorish, W. B. Raymond},
	date = {2012-12-06},
	langid = {english},
	keywords = {Mathematics / Algebra / Abstract, Mathematics / Geometry / Analytic, Mathematics / Geometry / General, Mathematics / Group Theory, Mathematics / Topology, Science / Physics / Mathematical \& Computational},
}

@article{fox,
	title = {Some Problems in Knot Theory},
	url = {https://cir.nii.ac.jp/crid/1573950399987265024},
	journaltitle = {Topology of 3-manifolds and related topics},
	author = {Fox, R. H.},
	urldate = {2023-07-11},
	date = {1962},
	publisher = {Prentice-Hall},
	file = {Snapshot:/home/jesse/Zotero/storage/IER4NKWT/1573950399987265024.html:text/html},
}

@book{penrose,
	location = {Cambridge},
	title = {Spinors and space-time. Volume 1, Two-spinor calculus and relativistic fields},
	isbn = {978-1-316-13894-6},
	series = {Cambridge monographs on mathematical physics},
	abstract = {This volume introduces and systematically develops the calculus of 2-spinors. This is the first detailed exposition of this technique which leads not only to a deeper understanding of the structure of space-time, but also provides shortcuts to some very tedious calculations. Many results are given here for the first time.},
	publisher = {University Press},
	author = {Penrose, Roger},
	editora = {Rindler, Wolfgang},
	editoratype = {collaborator},
	date = {1984},
	keywords = {Geometry, Differential, Mathematical physics, Space and time, Spinor analysis},
}

@book{hall,
	location = {New York, {NY}},
	title = {Quantum Theory for Mathematicians},
	volume = {267},
	isbn = {978-1-4614-7115-8 978-1-4614-7116-5},
	url = {https://link.springer.com/10.1007/978-1-4614-7116-5},
	series = {Graduate Texts in Mathematics},
	publisher = {Springer},
	author = {Hall, Brian C.},
	urldate = {2023-07-12},
	date = {2013},
	langid = {english},
	doi = {10.1007/978-1-4614-7116-5},
	keywords = {geometric quantization, Hilbert space, Lie groups, quantum mechanics, spectral theorem, Stone-von Neumann theorem, unbounded operators, {WKB} approximation},
	file = {Full Text PDF:/home/jesse/Zotero/storage/6EDSU3DY/Hall - 2013 - Quantum Theory for Mathematicians.pdf:application/pdf},
}

@article{weyl,
	title = {Quantenmechanik und Gruppentheorie},
	volume = {46},
	issn = {0044-3328},
	url = {https://doi.org/10.1007/BF02055756},
	doi = {10.1007/BF02055756},
	abstract = {Einleitung und Zusammenfassung. — I. Teil. Bedeutung der Repräsentation von physikalischen Größen durch Hermitesche Formen. § 1. Mathematische Grundbegriffe, die Hermiteschen Formen betreffend. § 2. Der physikalische Begriff des reinen Falles. § 3. Die physikalische Bedeutung der repräsentierenden Hermiteschen Form. § 4. Statistik der Gemenge. — {II}. Teil: Kinematik als Gruppe. § 5. Über Gruppen und ihre unitären Darstellungen. § 6. Übertragung auf kontinuierliche Gruppen. § 7. Ersatz der kanonischen Variablen durch die Gruppe. Das Elektron. § 8. Übergang zu Schrödingers Wellentheorie. — {III}. Teil. Das dynamische Problem. § 9. Das Gesetz der zeitlichen Veränderung. Die Zeitgesamtheit. § 10. Kinetische Energie und Coulombsche Kraft in der relativistischen Quantenmechanik. — Mathematischer Anhang.},
	pages = {1--46},
	number = {1},
	journaltitle = {Zeitschrift für Physik},
	shortjournal = {Z. Physik},
	author = {Weyl, H.},
	urldate = {2023-07-12},
	date = {1927-11-01},
	langid = {german},
	file = {Full Text PDF:/home/jesse/Zotero/storage/N29VVEVF/Weyl - 1927 - Quantenmechanik und Gruppentheorie.pdf:application/pdf},
}

@article{RT,
	title = {Invariants of 3-Manifolds via Link Polynomials and Quantum Groups},
	volume = {103},
	issn = {1432-1297},
	url = {https://doi.org/10.1007/BF01239527},
	doi = {10.1007/BF01239527},
	pages = {547--597},
	number = {1},
	journaltitle = {Inventiones mathematicae},
	shortjournal = {Invent Math},
	author = {Reshetikhin, N. and Turaev, V. G.},
	urldate = {2023-08-11},
	date = {1991-12-01},
	langid = {english},
	keywords = {Link Polynomial, Quantum Group},
	file = {Full Text PDF:/home/jesse/Zotero/storage/VS5JBIF6/Reshetikhin and Turaev - 1991 - Invariants of 3-manifolds via link polynomials and.pdf:application/pdf},
}
@misc {knotatlas,
  author = {Bar-Natan, Dror and Morrison, Scott and et al.},
  title = {The {K}not {A}tlas},
  url = {http://katlas.org},
}