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Topic: Heegaard splitting

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	Floer Homology Encyclopedia Article on Karr.net (Site not responding. Last check: 2007-11-06)
		Heegaard Floer homology also yields a knot invariant, which is formally similar to the combinatorially-defined Khovanov homology.
		Heegaard Floer homology is an invariant of a closed 3-manifold equipped with a spin structure.
		In the Heegaard splitting, Σ bounds two different 3-manifolds; the space of flat connections modulo gauge equivalence on each 3-manifold with boundary (equivalently, the space of connections on Σ that extend over each three manifold) is a Lagrangian submanifold of the space of connections on Σ.
	www.karr.net /Floer_homology/encyclopedia.htm (1945 words)

	Southeast Geometry Seminar
		Abstract: We will discuss the geometry of the curve complex associated to a closed orientable surface, and its relevance to the theory of Heegaard splittings of 3-manifolds.
		This discussion will include a definition of the distance of a Heegaard splitting.
		Our main result is that for a fixed pseudo-Anosov map φ defined on the boundary of a particular handlebody (and satisfying a certain necessary technical condition), the distance of the Heegaard splitting obtained by gluing two copies of the handlebody using the iterate φ
	www.math.uab.edu /sgs/sgs8 (658 words)

	published
		This paper generalizes the definition of a Heegaard splitting to unify the concepts of thin position for 3-manifolds, thin position for knots, and normal and almost normal surface theory.
		Critical Heegaard Surfaces and Index 2 Minimal Surfaces, in Proceedings of the Conference on Heegaard splittings and Dehn surgeries of 3-manifolds, Kyoto (Japan), July 2001.
		Hempel's definition of the distance of a Heegaard surface generalizes to a complexity for a knot which is in bridge position with respect to a Heegaard surface.
	pzacad.pitzer.edu /~dbachman/Papers/published.html (886 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		A Heegaard splitting of a closed 3-manifold is a decomposition of the 3-manifold into two handlebodies; a handlebody being a standard "doughnut" with one or more holes.
		Given constructions such as these, Heegaard splittings were long considered to be a type of superficial 3-manifold structure.
		The classification theorem for splittings of S^3 says that this tree is a stalk whose sole leaf is the genus 0 splitting.
	www.math.niu.edu /~rusin/known-math/99/3mflds (653 words)

	Reference.com/Encyclopedia/Heegaard splitting
		In the mathematical field of geometric topology, a Heegaard splitting is a special structure on a 3-manifold that results from dividing it into two handlebodies.
		Stablization: Given an Heegaard splitting H in M the stabilization of H is formed by taking the connected sum of the pair
		This result was extended by William Meeks to flat manifolds, except he proves that an embedded minimal surface in a flat three-manifold is either a Heegaard surface or totally geodesic.
	www.reference.com /browse/wiki/Heegaard_splitting (1306 words)

	Geometry Seminar, TBA (Site not responding. Last check: 2007-11-06)
		Abstract: It is well known that every compact orientable 3-manifold admits a Heegaard splitting.
		An important problem in studying 3-manifolds is to use "combinatorics" of the Heegaard splitting and obtain information about the topology of the 3-manifold.
		In particular, we expect a 3-manifold with a "complicated" splitting to have "rigid" structure.
	www.math.uconn.edu /~ratzkin/geom-seminar/spring2005/hossein.html (74 words)

	Atlas: Heegaard splittings and group presentations by Youn W. Lee (Site not responding. Last check: 2007-11-06)
		Associated to a Heegaard splitting of a 3-manifold, there exists a natural presentation of the fundamental group of the manifold.
		We study such presentations of Heegaard splittings of the 3-spere.
		We also describe a correspondence between Heegaard splittings of the 3-sphere and collections of simple arcs in the 3-ball and show that a 2-handle sliding is equivalent to an arc sliding.
	atlas-conferences.com /cgi-bin/abstract/cabg-06 (105 words)

	Preprints and Presentations
		Intended crystallographic benefits include new methods for visualization of space groups and crystal structures, analysis of the thermal motion patterns seen in ORTEP drawings, and a classification scheme for crystal structures based on their Heegaard splitting properties.
		Fundamental Group of a Euclidean 3-Orbifold by Carroll K. Johnson was presented at the ACA Annual Meeting, Buffalo, NY, May 22-27, 1999.
		Heegaard Splitting of Critical Nets on Orbifolds by Carroll K. Johnson and Michael N. Burnett was presented at the
	www.ornl.gov /sci/ortep/topology/preprint.html (503 words)

	COLLOQUIUM SCHEDULE OF THE DEPARTMENT OF MATHEMATICS AND STATISTICS (Site not responding. Last check: 2007-11-06)
		While this technique is quite old, there are fundamental questions about Heegaard splittings which remain largely unanswered.
		For example, is is unknown how quickly two Heegaard splittings of a given 3-manifold can be made the same via a certain basic move called stabilization.
		We focus on the processes generated by dissipative flows, which are known to have a mixed moving average representation, and we restrict our attention to regular moving averages with non-negative kernels.
	unr.edu /homepage/mathdept/colloq.html (619 words)

	the pretzel page
		Pretzel is a six-minute computer animation created to illustrate the proof of a thoerem about Heegaard splittings of three-manifolds ([Se]).This page contains clips from the video along with a sketch of the proof of the theorem.
		is the spine of an irreducible Heegaard splitting of M.
		Manipulating the spine by edge slides does not change the Heegaard splitting it represents (it is just an isotopy of the Heegaard surface).
	facweb.cs.depaul.edu /esedgwick/pretzel/pretzel.html (560 words)

	Alternate Heegaard genus bounds distance
		Suppose M is a compact orientable irreducible 3-manifold with Heegaard splitting surfaces P and Q. Then either Q is isotopic to a possibly stabilized or boundary-stabilized copy of P or the distance d(P)<= 2genus (Q).
		More generally, if P and Q are bicompressible but weakly incompressible connected closed separating surfaces in M then either P and Q can be well-separated or P and Q are isotopic or d(P)<= 2genus (Q).
		M Scharlemann and M Tomova, "Alternate Heegaard genus bounds distance" (2006).
	repositories.cdlib.org /postprints/1711 (115 words)

	3-manifold - Wikipedia, the free encyclopedia
		A key idea in the theory is to study a 3-manifold by considering special surfaces embedded in it.
		One can choose the surface to be nicely placed in the 3-manifold, which leads to the idea of an incompressible surface and the theory of Haken manifolds, or one can choose the complementary pieces to be as nice as possible, leading to structures such as Heegaard splittings, which are useful even in the non-Haken case.
		Thurston's contributions to the theory allow one to also consider, in many cases, the additional structure given by a particular Thurston model geometry (of which there are eight).
	en.wikipedia.org /wiki/3-manifold (473 words)

	Caltech Authors - Heegaard gradient and virtual fibers
		We show that if a closed hyperbolic 3-manifold has infinitely many finite covers of bounded Heegaard genus, then it is virtually fibered.
		Furthermore, we can replace the assumption that the covers have bounded Heegaard genus with the weaker hypotheses that the Heegaard splittings for the covers have Heegaard gradient zero, and also bounded width, in the sense of Scharlemann-Thompson thin position for Heegaard splittings.
		You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.
	authors.library.caltech.edu /1175 (196 words)

	/usr/local/info/math/sem_coll.html (Site not responding. Last check: 2007-11-06)
		Abstract: If a compact, fibered 3-manifold M has a 1-relator presentation, then the presentation is induced by a Heegaard splitting.
		M is equal to the restricted Heegaard genus of M in this situation.
		Abstract: In this talk we shall briefly introduce Heegaard Floer homology for 3-manifolds and knot Floer homology for knots in 3-manifolds.
	www.math.buffalo.edu /sem_coll.html (1331 words)

	Workshop on Three-dimensional Geometry and Topology
		These invariants are constructed by using Heegaard diagrams and studying Lagrangian Floer homology in the symmetric product of the Heegaard surface.
		Let M be a hyperbolic manifold, M = H \cup H' a Heegaard splitting and d_P(H,H') the distance in the pants-complex between the handlebody sets corresponding to H and H'.
		The appearing constants depend only on the genus of the Heegaard splitting.
	www.maths.ox.ac.uk /~lackenby/workshop.html (1991 words)

	Completely Tubing Compressible Tangles and Standard Graphs in Genus One 3-Manifolds (ResearchIndex) (Site not responding. Last check: 2007-11-06)
		A 1-vertex graph # in a 3manifold M with a genus 1 Heegaard splitting is standard if it consists of one or two parallel sets of core curves lying in the Heegaard splitting solid tori of M in the standard way.
		3 Scindements de Heegaard des espaces lenticulaires (context) - Bonahon, Otal - 1982
		1 The classification of Heegaard splittings (context) - Schultens - 1993
	citeseer.ist.psu.edu /wu00completely.html (382 words)

	Math arXiv: Search results (Site not responding. Last check: 2007-11-06)
		math.GT/0307231 Automorphisms of the 3-sphere that preserve a genus two Heegaard splitting.
		math.GT/9903078 Annuli in generalized Heegaard splittings and degeneration of tunnel number.
		math.GT/9803157 The structure of a solvmanifold's Heegaard splittings.
	front.math.ucdavis.edu /author/Scharlemann-M* (226 words)

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