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The four-genus of connected sums of torus knots
| Content Provider | Scilit |
|---|---|
| Author | Livingston, Charles Cott, Cornelia A. V. A. N. |
| Copyright Year | 2017 |
| Description | We study the four-genus of linear combinations of torus $knots:g_{4}$(aT(p, q) #-bT(p′, q′)). Fixing positivep, q, p′, andq′, our focus is on the behavior of the four-genus as a function of positiveaandb. Three types of examples are presented: in the first, for allaandbthe four-genus is completely determined by the Tristram–Levine signature function; for the second, the recently defined Upsilon function of Ozsváth–Stipsicz–Szabó determines the four-genus for allaandb; for the third, a surprising interplay between signatures and Upsilon appears. |
| Related Links | http://arxiv.org/pdf/1508.01455 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/D3C5AD26FCF6756FCFF3A58405C2BFB5/S0305004117000342a.pdf/div-class-title-the-four-genus-of-connected-sums-of-torus-knots-div.pdf |
| Ending Page | 550 |
| Page Count | 20 |
| Starting Page | 531 |
| ISSN | 03050041 |
| e-ISSN | 14698064 |
| DOI | 10.1017/s0305004117000342 |
| Journal | Mathematical Proceedings of the Cambridge Philosophical Society |
| Issue Number | 3 |
| Volume Number | 164 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2018-05-01 |
| Access Restriction | Open |
| Subject Keyword | Mathematical Proceedings of the Cambridge Philosophical Society Applied Mathematics Four Genus |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
