J. Hass and A. Thompson :
“A necessary and sufficient condition for a 3-manifold to have Heegaard genus one ,”
Proc. Am. Math. Soc.
107 : 4
(December 1989 ),
pp. 1107–1110 .
MR
984792
Zbl
0694.57006
article
Abstract
People
BibTeX
@article {key984792m,
AUTHOR = {Hass, Joel and Thompson, Abigail},
TITLE = {A necessary and sufficient condition
for a 3-manifold to have {H}eegaard
genus one},
JOURNAL = {Proc. Am. Math. Soc.},
FJOURNAL = {Proceedings of the American Mathematical
Society},
VOLUME = {107},
NUMBER = {4},
MONTH = {December},
YEAR = {1989},
PAGES = {1107--1110},
DOI = {10.2307/2047674},
NOTE = {MR:984792. Zbl:0694.57006.},
ISSN = {0002-9939},
}
J. Hass and A. Thompson :
“Neon bulbs and the unknotting of arcs in manifolds ,”
J. Knot Theor. Ramif.
6 : 2
(April 1997 ),
pp. 235–242 .
MR
1452439
Zbl
0886.57003
article
Abstract
People
BibTeX
@article {key1452439m,
AUTHOR = {Hass, Joel and Thompson, Abigail},
TITLE = {Neon bulbs and the unknotting of arcs
in manifolds},
JOURNAL = {J. Knot Theor. Ramif.},
FJOURNAL = {Journal of Knot Theory and its Ramifications},
VOLUME = {6},
NUMBER = {2},
MONTH = {April},
YEAR = {1997},
PAGES = {235--242},
DOI = {10.1142/S0218216597000157},
NOTE = {MR:1452439. Zbl:0886.57003.},
ISSN = {0218-2165},
}
C. Adams, J. Hass, and A. Thompson :
How to ace calculus: The streetwise guide .
W. H. Freeman (New York ),
1998 .
book
People
BibTeX
@book {key10944033,
AUTHOR = {Adams, Colin and Hass, Joel and Thompson,
Abigail},
TITLE = {How to ace calculus: {T}he streetwise
guide},
PUBLISHER = {W. H. Freeman},
ADDRESS = {New York},
YEAR = {1998},
PAGES = {x+230},
ISBN = {9780716731603},
}
C. Adams, J. Hass, and A. Thompson :
How to ace the rest of calculus: The streetwise guide .
W. H. Freeman (New York ),
2001 .
book
People
BibTeX
@book {key75201467,
AUTHOR = {Adams, Colin and Hass, Joel and Thompson,
Abigail},
TITLE = {How to ace the rest of calculus: {T}he
streetwise guide},
PUBLISHER = {W. H. Freeman},
ADDRESS = {New York},
YEAR = {2001},
PAGES = {ix+272},
ISBN = {9780716741749},
}
J. Hass, J. H. Rubinstein, and A. Thompson :
“Knots and \( k \) -width ,”
Geom. Dedicata
143 : 7
(December 2009 ),
pp. 7–18 .
MR
2576289
Zbl
1189.57005
ArXiv
math/0604256
article
Abstract
People
BibTeX
@article {key2576289m,
AUTHOR = {Hass, Joel and Rubinstein, J. Hyam and
Thompson, Abigail},
TITLE = {Knots and \$k\$-width},
JOURNAL = {Geom. Dedicata},
FJOURNAL = {Geometriae Dedicata},
VOLUME = {143},
NUMBER = {7},
MONTH = {December},
YEAR = {2009},
PAGES = {7--18},
DOI = {10.1007/s10711-009-9368-z},
NOTE = {ArXiv:math/0604256. MR:2576289. Zbl:1189.57005.},
ISSN = {0046-5755},
}
J. Hass, A. Thompson, and W. Thurston :
“Stabilization of Heegaard splittings ,”
Geom. Topol.
13 : 4
(2009 ),
pp. 2029–2050 .
MR
2507114
Zbl
1177.57018
ArXiv
0802.2145
article
Abstract
People
BibTeX
@article {key2507114m,
AUTHOR = {Hass, Joel and Thompson, Abigail and
Thurston, William},
TITLE = {Stabilization of {H}eegaard splittings},
JOURNAL = {Geom. Topol.},
FJOURNAL = {Geometry \& Topology},
VOLUME = {13},
NUMBER = {4},
YEAR = {2009},
PAGES = {2029--2050},
DOI = {10.2140/gt.2009.13.2029},
NOTE = {ArXiv:0802.2145. MR:2507114. Zbl:1177.57018.},
ISSN = {1465-3060},
}
J. Hass and A. Thompson :
“Is it knotted? ,”
pp. 129–135
in
Expeditions in mathematics .
Edited by T. Shubin, D. F. Hayes, and G. L. Alexanderson .
MAA Spectrum 68 .
Mathematical Association of America (Washington, DC ),
2011 .
incollection
People
BibTeX
@incollection {key94249627,
AUTHOR = {Hass, Joel and Thompson, Abigail},
TITLE = {Is it knotted?},
BOOKTITLE = {Expeditions in mathematics},
EDITOR = {Shubin, Tatiana and Hayes, David F.
and Alexanderson, Gerald L.},
SERIES = {MAA Spectrum},
NUMBER = {68},
PUBLISHER = {Mathematical Association of America},
ADDRESS = {Washington, DC},
YEAR = {2011},
PAGES = {129--135},
ISBN = {9780883855713},
}
J. Hass, A. Thompson, and A. Tsvietkova :
“The number of surfaces of fixed genus in an alternating link complement ,”
Int. Math. Res. Not.
2017 : 6
(March 2017 ),
pp. 1611–1622 .
MR
3658176
ArXiv
1508.03680
article
Abstract
People
BibTeX
Let \( L \) be a prime alternating link with \( n \) crossings. We show that for each fixed \( g \) , the number of genus \( g \) incompressible surfaces in the complement of \( L \) is bounded by an explicitly given polynomial in \( n \) . Previous bounds were exponential in \( n \) .
@article {key3658176m,
AUTHOR = {Hass, Joel and Thompson, Abigail and
Tsvietkova, Anastasiia},
TITLE = {The number of surfaces of fixed genus
in an alternating link complement},
JOURNAL = {Int. Math. Res. Not.},
FJOURNAL = {International Mathematics Research Notices},
VOLUME = {2017},
NUMBER = {6},
MONTH = {March},
YEAR = {2017},
PAGES = {1611--1622},
DOI = {10.1093/imrn/rnw075},
NOTE = {ArXiv:1508.03680. MR:3658176.},
ISSN = {1073-7928},
}
J. Hass, A. Thompson, and A. Tsvietkova :
“Alternating links have at most polynomially many Seifert
surfaces of fixed genus ,”
Indiana Univ. Math. J.
70 : 2
(2021 ),
pp. 525–534 .
MR
4257618
article
Abstract
People
BibTeX
Let \( L \) be a non-split prime alternating link with \( n > 0 \) crossings. We show that for each fixed \( g \) , the number of genus-\( g \) Seifert surfaces for \( L \) is bounded by an explicitly given polynomial in \( n \) . The result also holds for all spanning surfaces of fixed Euler characteristic. Previously known bounds were exponential.
@article {key4257618m,
AUTHOR = {Hass, Joel and Thompson, Abigail and
Tsvietkova, Anastasiia},
TITLE = {Alternating links have at most polynomially
many {S}eifert surfaces of fixed genus},
JOURNAL = {Indiana Univ. Math. J.},
FJOURNAL = {Indiana University Mathematics Journal},
VOLUME = {70},
NUMBER = {2},
YEAR = {2021},
PAGES = {525--534},
DOI = {10.1512/iumj.2021.70.8350},
URL = {https://doi.org/10.1512/iumj.2021.70.8350},
NOTE = {MR:4257618.},
ISSN = {0022-2518,1943-5258},
}
J. Hass, A. Thompson, and A. Tsvietkova :
“Tangle decompositions of alternating link complements ,”
Illinois J. Math.
65 : 3
(2021 ),
pp. 533–545 .
MR
4312193
article
Abstract
People
BibTeX
Decomposing knots and links into tangles is a useful technique for understanding their properties. The notion of prime tangles was introduced by Kirby and Lickorish; Lickorish proved that by summing prime tangles one obtains a prime link. In a similar spirit, summing two prime alternating tangles will produce a prime alternating link if summed correctly with respect to the alternating property. Given a prime alternating link, we seek to understand whether it can be decomposed into two prime tangles, each of which is alternating. We refine results of Menasco and Thistlethwaite to show that if such a decomposition exists, either it is visible in an alternating link diagram or the link is of a particular form, which we call a pseudo-Montesinos link.
@article {key4312193m,
AUTHOR = {Hass, Joel and Thompson, Abigail and
Tsvietkova, Anastasiia},
TITLE = {Tangle decompositions of alternating
link complements},
JOURNAL = {Illinois J. Math.},
FJOURNAL = {Illinois Journal of Mathematics},
VOLUME = {65},
NUMBER = {3},
YEAR = {2021},
PAGES = {533--545},
DOI = {10.1215/00192082-9291846},
URL = {https://doi.org/10.1215/00192082-9291846},
NOTE = {MR:4312193.},
ISSN = {0019-2082,1945-6581},
}