Open Access. Powered by Scholars. Published by Universities.®
- Discipline
- Keyword
Articles 1 - 3 of 3
Full-Text Articles in Algebraic Geometry
Drawing A Triangle On The Thurston Model Of Hyperbolic Space, Curtis D. Bennett, Blake Mellor, Patrick D. Shanahan
Drawing A Triangle On The Thurston Model Of Hyperbolic Space, Curtis D. Bennett, Blake Mellor, Patrick D. Shanahan
Mathematics Faculty Works
In looking at a common physical model of the hyperbolic plane, the authors encountered surprising difficulties in drawing a large triangle. Understanding these difficulties leads to an intriguing exploration of the geometry of the Thurston model of the hyperbolic plane. In this exploration we encounter topics ranging from combinatorics and Pick’s Theorem to differential geometry and the Gauss-Bonnet Theorem.
Epimorphisms And Boundary Slopes Of 2–Bridge Knots, Jim Hoste, Patrick D. Shanahan
Epimorphisms And Boundary Slopes Of 2–Bridge Knots, Jim Hoste, Patrick D. Shanahan
Mathematics Faculty Works
In this article we study a partial ordering on knots in S3 where K1≥K2 if there is an epimorphism from the knot group of K1 onto the knot group of K2 which preserves peripheral structure. If K1 is a 2–bridge knot and K1≥K2, then it is known that K2 must also be 2–bridge. Furthermore, Ohtsuki, Riley and Sakuma give a construction which, for a given 2–bridge knot Kp∕q, produces infinitely many 2–bridge knots Kp′/q′ with Kp′∕q′≥Kp∕q. After characterizing all 2–bridge knots …
Linked Exact Triples Of Triangulated Categories And A Calculus Of T-Structures, Michael Berg
Linked Exact Triples Of Triangulated Categories And A Calculus Of T-Structures, Michael Berg
Mathematics Faculty Works
We introduce a new formalism of exact triples of triangulated categories arranged in certain types of diagrams. We prove that these arrangements are well-behaved relative to the process of gluing and ungluing t-structures defined on the indicated categories and we connect our con. structs to· a problem (from number theory) involving derived categories. We also briefly address a possible connection with a result of R. Thomason.