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In this talk, we will develop the theory of generalized bridge trisections for smoothly embedded closed surfaces in smooth, closed four-manifolds. The main result is that any such surface can be isotoped to lie in bridge trisected position with respect to a given trisection of the ambient four-manifold. In the setting of knotted surfaces in the four-sphere, this gives a diagrammatic calculus that offers a promising new approach to four-dimensional knot theory. However, the theory extends to other ambient four-manifolds, and we will pay particular attention to the setting of complex curves in simple complex surfaces, where the theory produces surprisingly satisfying pictures and leads to interesting results about trisections of complex surfaces.
This talk is based on various joint works with Dave Gay, Peter Lambert-Cole, and Alex Zupan. In this talk, we will develop the theory of generalized bridge trisections for smoothly embedded closed surfaces in smooth, closed four-manifolds. The main result is that any such surface can be isotoped to lie in bridge trisected position with respect to a given trisection of the ambient four-manifold. In the setting of knotted surfaces in the four-sphere, this gives a diagrammatic calculus that offers a promising new approach to four-...

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Documents 57Q45 | enregistrements trouvés : 57

Bridge trisections of knotted surfaces in four-manifolds​ Meier, Jeffrey | CIRM H Nouveau

Topology of algebraic varieties and singularities.Conference in honor of Anatoly Libgober's 60th birthdayHuesca # june 22-26, 2009 Cogolludo-Agustin, José Ignacio ; Hironaka, Eriko | American Mathematical Society;Real Sociedad Matematica Espanola 2011 Nouveau

Topological and geometrical methods in field theorysecond international symposium on...at the paasikivi-institutemay 26- june 1 Mickelsson, Jouko ; Pekonen, Osmo | World Scientific 1992 Nouveau

Noeuds,tresses et singularitescomptes rendus du seminaire tenu aux plans-sur-bex suisse en mars 1982 | Universite de Genève 1983 Nouveau

Modern methods in complex analysisThe conference was held in fine Hall at Princeton University from March 16 to March 20, 1992 in honor of Gunning and Kohn Bloom, Thomas ; Catlin, David ; D'Angelo, John P. ; Siu, Yum-Tong | Princeton University Press 1995 Nouveau

Lectures on geometry.Papers based on lectures delivered at Clay mathematics institute. Witten, Edward ; Lackenby, Marc ; Bridson, Martin, R. ; Hofer, Helmut H. W. ; Pandharipande, Rahul ; Woodhouse, N. M. J. | Oxford University Press 2017 Nouveau

Knots in Poland III, Part III.Proceedings of the 3rd conferenceWarsaw # July 18-25, 2010Bedlewo # July 25-August 4, 2010 Przytycki, Jozef H. ; Traczyk, Pawel | Polish Academy of Sciences 2014 Nouveau

Knots in Poland III, Part I.Proceedings of the 3rd conferenceWarsaw # July 18-25, 2010Bedlewo # July 25-August 4, 2010 Przytycki, Jozef H. ; Traczyk, Pawel | Polish Academy of Sciences 2014 Nouveau

Knot theory and its applications.ICTS programMohali # December 10-20, 2013 Gongopadhyay, Krishnendu ; Mishra, Rama | American Mathematical Society 2016 Nouveau

Knot theory :proceedings held at plan-sur-bex Haussmann, K. C. | Springer-Verlag 1978 Nouveau

Geometry and topology down under:a conference in honour of Hyam RubinsteinMelbourne # july 11-22, 2011 Hodgson, Craig D. ; Jaco, William H. ; Scharlemann, Martin G. ; Tillmann, Stephan | American Mathematical Society 2013 Nouveau

Computational problems in abstract algebraproceedings of a conferenceAug. 29 - Sept. 2 Howlett, J. ; Leech, John, | Pergamon Press 1970 Nouveau

Virtual knots:the state of the art Manturov, Vassily Olegovich ; Ilyutko, Denis Petrovich | World Scientific 2013 Nouveau

Torsion et type simple d'homotopieexposés faits au séminaire de topologie de l'université de Lausane De Rham, G. ; Maumary, S. ; Kervaire, M. | Springer-Verlag 1967 Nouveau

Topological invariants of quasi-ordinary singularities,embedded topological CLASSIFICATION OF QUASI-ORDINARY SINGULARITIES Lipman, Joseph ; Gau, Yih-Nan | American Mathematical Society 1988 Nouveau

Three-dimensional link theory and invariants of plane curve singularities Eisenbud, David ; Neumann, Walter | Princeton University Press 1985 Nouveau

The structure of the rational concordance group of knots Choon Cha, Jae | Amercian Mathematical Society 2007 Nouveau

The mathematics of knots:theory and application.Based on the themes of the Heidelberg knot theory semester, held in winter 2008/09 Banagl, Markus ; Vogel, Denis | Springer;The Mathematics Center Heidelberg;The Interdisciplinary Center for Scientific Computing 2011 Nouveau

The knot bookan elementary introduction to the mathematical theory of knots Adams, Colin C. | W.H. Freeman and Co. 1994 Nouveau

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Bridge trisections of knotted surfaces in four-manifolds Meier, Jeffrey | CIRM H Nouveau

Topology of algebraic varieties and singularities.
Conference in honor of Anatoly Libgober's 60th birthday
Huesca # june 22-26, 2009 Cogolludo-Agustin, José Ignacio ; Hironaka, Eriko | American Mathematical Society;Real Sociedad Matematica Espanola 2011 Nouveau

Topological and geometrical methods in field theory
second international symposium on...
at the paasikivi-institute
may 26- june 1 Mickelsson, Jouko ; Pekonen, Osmo | World Scientific 1992 Nouveau

Noeuds,tresses et singularites
comptes rendus du seminaire tenu aux plans-sur-bex suisse en mars 1982 | Universite de Genève 1983 Nouveau

Modern methods in complex analysis
The conference was held in fine Hall at Princeton University from March 16 to March 20, 1992 in honor of Gunning and Kohn Bloom, Thomas ; Catlin, David ; D'Angelo, John P. ; Siu, Yum-Tong | Princeton University Press 1995 Nouveau

Lectures on geometry.
Papers based on lectures delivered at Clay mathematics institute. Witten, Edward ; Lackenby, Marc ; Bridson, Martin, R. ; Hofer, Helmut H. W. ; Pandharipande, Rahul ; Woodhouse, N. M. J. | Oxford University Press 2017 Nouveau

Knots in Poland III, Part III.
Proceedings of the 3rd conference
Warsaw # July 18-25, 2010
Bedlewo # July 25-August 4, 2010 Przytycki, Jozef H. ; Traczyk, Pawel | Polish Academy of Sciences 2014 Nouveau

Knots in Poland III, Part I.
Proceedings of the 3rd conference
Warsaw # July 18-25, 2010
Bedlewo # July 25-August 4, 2010 Przytycki, Jozef H. ; Traczyk, Pawel | Polish Academy of Sciences 2014 Nouveau

Knot theory and its applications.
ICTS program
Mohali # December 10-20, 2013 Gongopadhyay, Krishnendu ; Mishra, Rama | American Mathematical Society 2016 Nouveau

Knot theory :
proceedings held at plan-sur-bex Haussmann, K. C. | Springer-Verlag 1978 Nouveau

Geometry and topology down under:
a conference in honour of Hyam Rubinstein
Melbourne # july 11-22, 2011 Hodgson, Craig D. ; Jaco, William H. ; Scharlemann, Martin G. ; Tillmann, Stephan | American Mathematical Society 2013 Nouveau

Computational problems in abstract algebra
proceedings of a conference
Aug. 29 - Sept. 2 Howlett, J. ; Leech, John, | Pergamon Press 1970 Nouveau

Virtual knots:
the state of the art Manturov, Vassily Olegovich ; Ilyutko, Denis Petrovich | World Scientific 2013 Nouveau

Torsion et type simple d'homotopie
exposés faits au séminaire de topologie de l'université de Lausane De Rham, G. ; Maumary, S. ; Kervaire, M. | Springer-Verlag 1967 Nouveau

The mathematics of knots:
theory and application.
Based on the themes of the Heidelberg knot theory semester, held in winter 2008/09 Banagl, Markus ; Vogel, Denis | Springer;The Mathematics Center Heidelberg;The Interdisciplinary Center for Scientific Computing 2011 Nouveau

The knot book
an elementary introduction to the mathematical theory of knots Adams, Colin C. | W.H. Freeman and Co. 1994 Nouveau