Patrick D. Shanahan

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All published works

Action	Title	Year	Authors
+ PDF Chat	Average crosscap number of a 2-bridge knot	2025	Moshe Cohen Thomas Kindred Adam M. Lowrance Patrick D. Shanahan Cornelia A. Van Cott
+ PDF Chat	On the nonorientable 4-genus of double twist knots	2023	Jim Hoste Patrick D. Shanahan Cornelia A. Van Cott
+	On the nonorientable 4-genus of double twist knots	2022	Jim Hoste Patrick D. Shanahan Cornelia A. Van Cott
+ PDF Chat	Crosscap number and epimorphisms of two-bridge knot groups	2021	Jim Hoste Patrick D. Shanahan Cornelia A. Van Cott
+	Crosscap number and the partial order on two-bridge knots	2020	Jim Hoste Patrick D. Shanahan Cornelia A. Van Cott
+	Crosscap number and epimorphisms of two-bridge knot groups	2020	Jim Hoste Patrick D. Shanahan Cornelia A. Van Cott
+	Crosscap number and epimorphisms of two-bridge knot groups	2020	Jim Hoste Patrick D. Shanahan Cornelia A. Van Cott
+ PDF Chat	Remarks on Suzuki’s knot epimorphism number	2019	Jim Hoste Joshua Ocana Mercado Patrick D. Shanahan
+ PDF Chat	Finite n-quandles of torus and two-bridge links	2019	Alissa S. Crans Blake Mellor Patrick D. Shanahan Jim Hoste
+	Remarks on Suzuki's epimorphism number	2019	Patrick D. Shanahan
+	Remarks on Suzuki's Knot Epimorphism Number	2018	Jim Hoste Joshua Ocana Mercado Patrick D. Shanahan
+	Finite $n$-quandles of torus and two-bridge links	2018	Alissa S. Crans Jim Hoste Blake Mellor Patrick D. Shanahan
+ PDF Chat	An enumeration process for racks	2018	Jim Hoste Patrick D. Shanahan
+	Remarks on Suzuki's Knot Epimorphism Number	2018	Jim Hoste Joshua Ocana Mercado Patrick D. Shanahan
+	Finite $n$-quandles of torus and two-bridge links	2018	Alissa S. Crans Jim Hoste Blake Mellor Patrick D. Shanahan
+ PDF Chat	Links with finite n–quandles	2017	Jim Hoste Patrick D. Shanahan
+	An enumeration process for racks	2017	Jim Hoste Patrick D. Shanahan
+	An enumeration process for racks	2017	Jim Hoste Patrick D. Shanahan
+ PDF Chat	Involutory quandles of (2,2,r)-Montesinos links	2016	Jim Hoste Patrick D. Shanahan
+	Involutory quandles of (2,2,r)-Montesinos links	2016	Jim Hoste Patrick D. Shanahan
+	Involutory quandles of (2,2,r)-Montesinos links	2016	Jim Hoste Patrick D. Shanahan
+	Complex Analysis: A First Course with Applications	2013	Dennis G. Zill Patrick D. Shanahan
+	Complex Analysis	2013	Dennis G. Zill Patrick D. Shanahan
+ PDF Chat	TWISTED ALEXANDER POLYNOMIALS OF 2-BRIDGE KNOTS	2012	Jim Hoste Patrick D. Shanahan
+	Twisted Alexander polynomials of 2-bridge knots	2012	Jim Hoste Patrick D. Shanahan
+	Introductory College Mathematics	2012	Patrick D. Shanahan
+ PDF Chat	UPPER BOUNDS IN THE OHTSUKI–RILEY–SAKUMA PARTIAL ORDER ON 2-BRIDGE KNOTS	2012	Scott Garrabrant Jim Hoste Patrick D. Shanahan
+	Twisted Alexander polynomials of 2-bridge knots	2012	Jim Hoste Patrick D. Shanahan
+	Two-bridge knots with common ORS covers	2010	Jim Hoste Patrick D. Shanahan
+	Upper bounds in the Ohtsuki-Riley-Sakuma partial order on 2-bridge knots	2010	Scott Garrabrant Jim Hoste Patrick D. Shanahan
+	Epimorphisms and boundary slopes of 2–bridge knots	2010	Jim Hoste Patrick D. Shanahan
+	Drawing a Triangle on the Thurston Model of Hyperbolic Space	2010	Curtis D. Bennett Blake Mellor Patrick D. Shanahan
+	Upper bounds in the Ohtsuki-Riley-Sakuma partial order on 2-bridge knots	2010	Scott Garrabrant Jim Hoste Patrick D. Shanahan
+	Boundary slopes of 2-bridge links determine the crossing number	2007	Jim Hoste Patrick D. Shanahan
+ PDF Chat	Computing boundary slopes of 2-bridge links	2007	Jim Hoste Patrick D. Shanahan
+	Boundary slopes of 2-bridge links determine the crossing number	2006	Jim Hoste Patrick D. Shanahan
+	REMARKS ON SOME HYPERBOLIC INVARIANTS OF 2-BRIDGE KNOTS	2005	Jim Hoste Patrick D. Shanahan
+ PDF Chat	COMMENSURABILITY CLASSES OF TWIST KNOTS	2005	Jim Hoste Patrick D. Shanahan
+	Computing boundary slopes of 2-bridge links	2005	Jim Hoste Patrick D. Shanahan
+	A FORMULA FOR THE A-POLYNOMIAL OF TWIST KNOTS	2004	Jim Hoste Patrick D. Shanahan
+	Commensurability classes of twist knots	2003	Jim Hoste Patrick D. Shanahan
+	TRACE FIELDS OF TWIST KNOTS	2001	Jim Hoste Patrick D. Shanahan
+	Cyclic Dehn surgery and the A-polynomial	2000	Patrick D. Shanahan
+	Three-Dimensional Representations of Punctured Torus Bundles	1997	Brian Mangum Patrick D. Shanahan
+ PDF Chat	On the signature of Grassmannians	1979	Patrick D. Shanahan
+	The Atiyah-Singer Index Theorem: An Introduction	1978	Patrick D. Shanahan
+	The atiyah-singer fixed point theorem	1978	Patrick D. Shanahan
+	Applications of the fixed point theorem	1978	Patrick D. Shanahan
+ PDF Chat	The Atiyah-Singer Index Theorem	1978	Patrick D. Shanahan
+	Addendum to “A Unified Proof of Several Basic Theorems of Real Analysis”	1974	Patrick D. Shanahan
+	Addendum to "A Unified Proof of Several Basic Theorems of Real Analysis"	1974	Patrick D. Shanahan
+	A Unified Proof of Several Basic Theorems of Real Analysis	1972	Patrick D. Shanahan

Common Coauthors

Coauthor	Papers Together
Jim Hoste	36
Cornelia A. Van Cott	7
Blake Mellor	4
Scott Garrabrant	3
Joshua Ocana Mercado	3
Alissa S. Crans	2
Dennis G. Zill	2
Curtis D. Bennett	1
Brian Mangum	1
Moshe Cohen	1
Adam M. Lowrance	1
Alissa S. Crans	1
Thomas Kindred	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Incompressible surfaces in 2-bridge knot complements	1985	Allen Hatcher William P. Thurston	8
+	RACKS AND LINKS IN CODIMENSION TWO	1992	Roger Fenn Colin Rourke	7
+	A classifying invariant of knots, the knot quandle	1982	David Joyce	7
+ PDF Chat	KNOT GROUP EPIMORPHISMS	2006	Daniel S. Silver Wilbur Whitten	6
+ PDF Chat	Epimorphisms between 2–bridge link groups	2008	Tomotada Ohtsuki Robert W. Riley Makoto Sakuma	6
+ PDF Chat	Involutory quandles of (2,2,r)-Montesinos links	2016	Jim Hoste Patrick D. Shanahan	5
+	An Algebraic Approach to Symmetry With Applications to Knot Theory	1979	David Joyce	5
+	A Partial Order in the Knot Table II	2008	Teruaki Kitano Masaaki Suzuki	4
+ PDF Chat	A practical method for enumerating cosets of a finite abstract group	1936	John A. Todd H. S. M. Coxeter	4
+	A Partial Order in the Knot Table	2005	Teruaki Kitano Masaaki Suzuki	4
+ PDF Chat	Ideal points and incompressible surfaces in two-bridge knot complements	1994	Tomotada Ohtsuki	4
+	NONABELIAN REPRESENTATIONS OF 2-BRIDGE KNOT GROUPS	1984	Robert W. Riley	4
+ PDF Chat	Simon’s conjecture for two-bridge knots	2010	Michel Boileau Steve Boyer Alan W. Reid Shicheng Wang	3
+	Knots and Links	2004	Peter R. Cromwell	3
+	Knot complements and groups	1987	Wilbur Whitten	3
+	de Gruyter Studies in Mathematics	2009	Carsten Carstensen G. Farkas Nicola Fusco Fritz Gesztesy Niels Jacob Zenghu Li Karl‐Hermann Neeb	3
+	Epimorphisms and boundary slopes of 2–bridge knots	2010	Jim Hoste Patrick D. Shanahan	3
+ PDF Chat	Epimorphisms between 2-bridge link groups: homotopically trivial simple loops on 2-bridge spheres	2011	Donghi Lee Makoto Sakuma	3
+ PDF Chat	A PARTIAL ORDER ON THE SET OF PRIME KNOTS WITH UP TO 11 CROSSINGS	2011	Keiichi Horie Teruaki Kitano Mineko Matsumoto Masaaki Suzuki	3
+ PDF Chat	The space of incompressible surfaces in a $2$-bridge link complement	1988	William Floyd Allen Hatcher	3
+ PDF Chat	UPPER BOUNDS IN THE OHTSUKI–RILEY–SAKUMA PARTIAL ORDER ON 2-BRIDGE KNOTS	2012	Scott Garrabrant Jim Hoste Patrick D. Shanahan	3
+	DISTRIBUTIVE GROUPOIDS IN KNOT THEORY	1984	Sergey V. Matveev	3
+ PDF Chat	Links with finite n–quandles	2017	Jim Hoste Patrick D. Shanahan	3
+	Crosscap numbers and the Jones polynomial	2015	Efstratia Kalfagianni Christine Ruey Shan Lee	2
+	Quandles	2015	Mohamed Elhamdadi Sam Nelson	2
+	ON THE 3-DIMENSIONAL BRIESKORN MANIFOLDS M(p,q,r)	1975	John Milnor	2
+	Genera of two-bridge knots and epimorphisms of their knot groups	2018	Masaaki Suzuki Anh T. Tran	2
+ PDF Chat	Commensurability and the character variety	1999	D. D. Long A. W. Reid	2
+	A FORMULA FOR THE A-POLYNOMIAL OF TWIST KNOTS	2004	Jim Hoste Patrick D. Shanahan	2
+	A partial order on the set of prime knots with up to 11 crossings	2009	Keiichi Horie Teruaki Kitano Mineko Matsumoto Masaaki Suzuki	2
+	A partial order in the knot table II	2008	Teruaki Kitano Masaaki Suzuki	2
+ PDF Chat	Crosscap numbers of pretzel knots	2009	Kazuhiro Ichihara Shigeru Mizushima	2
+ PDF Chat	On two-bridged knot polynomials	1979	Richard Hartley	2
+	Twisted Alexander polynomials and a partial order on the set of prime knots	2008	Teruaki Kitano Masaaki Suzuki	2
+ PDF Chat	Crosscap numbers of alternating knots via unknotting splices	2020	Thomas Kindred	2
+	Boundary slopes for Montesinos knots	1989	Allen Hatcher Ulrich Oertel	2
+	The branched cyclic coverings of 2 bridge knots and links	1982	Jerome Minkus	2
+ PDF Chat	AUTOMORPHISM GROUPS OF QUANDLES	2012	Mohamed Elhamdadi JENNIFER MACQUARRIE Ricardo Restrepo	2
+	A table of boundary slopes of Montesinos knots	2001	Nathan M. Dunfield	2
+	ON THE ARITHMETIC 2-BRIDGE KNOTS AND LINK ORBIFOLDS AND A NEW KNOT INVARIANT	1995	Hugh M. Hilden María Teresa Lozano José María Montesinos-Amilibia	2
+	A graph-theoretic approach to a partial order of knots and links	2010	Toshiki ENDO Tomoko Itoh Kouki Taniyama	2
+ PDF Chat	Introduction to Knot Theory.	1964	H. F. Trotter Richard H. Crowell Ralph H. Fox	2
+ PDF Chat	Plane curves associated to character varieties of 3-manifolds	1994	D. Cooper Marc Culler Henri Gillet D. D. Long Peter B. Shalen	2
+	TRACE FIELDS OF TWIST KNOTS	2001	Jim Hoste Patrick D. Shanahan	2
+ PDF Chat	A Partial Order of Knots	1989	Kouki Taniyama	2
+	Surgeries on one component of the Whitehead link are virtually fibered	2002	Christopher J. Leininger	2
+	Presentation length and Simon’s conjecture	2011	Ian Agol Yi Liu	2
+	Presentations of Groups	1997	David Linton Johnson	2
+ PDF Chat	Commensurability of 1-cusped hyperbolic 3-manifolds	2002	Danny Calegari Nathan M. Dunfield	2
+ PDF Chat	A classification of spanning surfaces for alternating links	2013	Colin Adams Thomas Kindred	2