Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Unknotted homology classes on unknotted surfaces in $ S\sp 3$


Author: Bruce Trace
Journal: Trans. Amer. Math. Soc. 318 (1990), 43-56
MSC: Primary 57M99; Secondary 57M25
MathSciNet review: 965303
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Suppose $ F$ is a closed, genus $ g$ surface which is standardly embedded in $ {S^3}$. Let $ \gamma $ denote a primitive element in $ {H_1}(F)$ which satisfies $ {\theta _F}(\gamma ,\gamma ) = 0$ where $ {\theta _F}$ is the Seifert pairing on $ F$. We obtain a number theoretic condition which is equivalent to $ \gamma $ being realizable by a curve (in $ F$) which is unknotted in $ {S^3}$. Various related observations are included.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 57M99, 57M25

Retrieve articles in all journals with MSC: 57M99, 57M25


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1990-0965303-9
PII: S 0002-9947(1990)0965303-9
Article copyright: © Copyright 1990 American Mathematical Society