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Some $3$–dimensional transverse $\mathbb{C}$–links (Constructions of higher-dimensional $\mathbb{C}$–links, I)

Lee Rudolph

Geometry & Topology Monographs 19 (2015) 367–413

arXiv: 1508.05073

Abstract

By use of a variety of techniques (most based on constructions of quasipositive knots and links, some old and others new), many smooth 3–manifolds are realized as transverse intersections of complex surfaces in 3 with strictly pseudoconvex 5–spheres. These manifolds not only inherit interesting intrinsic structures (eg, they have canonical Stein-fillable contact structures), they also have extrinsic structures of a knot-theoretical nature (eq, S3 arises in infinitely many distinct ways). This survey is not comprehensive; a number of questions are left open for future work.

Keywords
quasipositivity, contact structures on $3$–manifolds, topological aspects of Stein theory, graph manifolds
Mathematical Subject Classification 2010
Primary: 32Q28, 57M25, 57M27, 57R17
Secondary: 57Q45, 14B05
References
Publication
Received: 19 August 2015
Accepted: 19 August 2015
Published: 29 December 2015
Authors
Lee Rudolph
Mathematics and Computer Science
Clark University
Worcester, MA 01610-1477
USA