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Topic: Dehn twist

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Franz Bardon

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	Max Dehn - Wikipedia, the free encyclopedia
		In 1910 Dehn published a paper on three dimensional topology in which he introduced Dehn surgery and used it to construct homology spheres.
		In 1912 Dehn invented what is now known as Dehn's algorithm and used it in his work on the word and conjugacy problems for groups.
		In the early 1920's Dehn introduced the result that would come to be known as the Dehn-Nielsen theorem; its proof would be published in 1927 by Jakob Nielsen.
	en.wikipedia.org /wiki/Max_Dehn (441 words)

	Mapping class group - Wikipedia, the free encyclopedia
		We note that the non-extended mapping class group of any closed, orientable surface can be generated by Dehn twists.
		The four elements are the identity, a Dehn twist on the two-sided curve which does not bound a Mobius band, the y-homeomorphism of Lickorish, and the product of the twist and the y-homeomorphism.
		It is a nice exercise to show that the square of the Dehn twist is isotopic to the identity.
	en.wikipedia.org /wiki/Mapping_class_group (428 words)

	Abstracts of my papers
		It is proved that the stable commutator length of a Dehn twist in the mapping class group is positive and the tenth power of a Dehn twist about a nonseparating simple closed curve is a product of two commutators.
		As an application a new proof of the fact that the growth rate of a Dehn twist is linear is given.
		Other results are that every Dhen twist on a closed surface of genus at least three is the product of two commutators and no Dehn twist on any closed surface is equal to a single commutator.
	www.math.metu.edu.tr /~korkmaz/abstracts.html (1508 words)

	Mapping Class Groups REU Home Page
		In fact, the group generated by Dehn twists about separating curves is an important normal subgroup of the Torelli group, known as the Johnson kernel and denoted K
		To begin with, we consider three types of operations on compositions of Dehn twists about separating curves, all of which preserve the image of those twists under the Birman-Craggs-Johnson homomorphism.
		We observe that, at least in some cases, a finite sequence of these moves produces a Dehn twist about a trivial curve, demonstrating that the original composition of Dehn twists is in the BCJ kernel.
	www.math.cornell.edu /~brendle/REU/REUhome.html (971 words)

	ABSTRACT (Site not responding. Last check: 2007-10-23)
		It is a rather straightforward observation that this particular consequence of Kotschick's strong result is false for the extended mapping class group of S, in which the square of any right-handed Dehn twist is a commutator.
		Indeed, as we shall explain in this talk, for genus at least 3, a right handed Dehn twist about a nonseparating circle is a commutator of two pseudo-Anosov maps S ----> S.
		The failure of his result for the extended mapping class group indicates that this result depends upon "positivity" phenomena in the mapping class group, phenomena which is reflected through the connection between commutator relations in the mapping class group of S and Lefschetz fibrations over closed surfaces with generic fiber S
	www.mth.msu.edu /~mccarthy/topology.seminar/abstract.mccarthy.2.html (171 words)

	[No title] (Site not responding. Last check: 2007-10-23)
		In this talk I will compute the PFH when the diffeomorphism is the Dehn twist.
		The PFH of the Dehn twist is of particular interest because it ties into C. Taubes' program for studying the obstruction of symplectic structures on 4-manifolds.
		The PFH of a Dehn twist should also recover the Seiberg-Witten invariants of symplectic 4-manifolds using S.
	www.math.wayne.edu /~handel/topsem/topabstr/10.22.html (132 words)

	Citebase - The periodic Floer homology of a Dehn twist
		The periodic Floer homology of a Dehn twist
		The periodic Floer homology of a surface symplectomorphism, defined by the first author and M. Thaddeus, is the homology of a chain complex which is generated by certain unions of periodic orbits, and whose differential counts certain embedded pseudoholomorphic curves in R cross the mapping torus.
		It is conjectured to recover the Seiberg-Witten Floer homology of the mapping torus for most spin-c structures, and is related to a variant of contact homology.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/0410059 (165 words)

	Rabbit Movies (Site not responding. Last check: 2007-10-23)
		Douady's question of determining the Thurston equivalence class of the topological polynomial obtained by applying a Dehn twist to the rabbit polynomial.
		Twisting about the generator S of the mapping class group; here in low resolution; here with the moduli and dynamical spaces superposed
		Twisting about the generator T of the mapping class group; here in low resolution
	mad.epfl.ch /~laurent/pub/rabbit/index.html (272 words)

	natlie dehn - ResearchIndex document query (Site not responding. Last check: 2007-10-23)
		I g1.It is well known that M g1 is generated by Dehn twists.
		The Dehn twist Y acts on the (transformed) subsets E yk
		neighborhood of #M which restricts to a standard Dehn twist in each meridional annulus.
	citeseer.ist.psu.edu /cis?q=Natlie+Dehn (763 words)

	[No title] (Site not responding. Last check: 2007-10-23)
		definition of Dehn twist and proving that the oriented mapping class group of any closed oriented surface is generated by Dehn twists.
		proving that any closed 3-manifold is obtained by Dehn surgery along a link in the 3-sphere.
		Haken 3-manifolds with an infinite cyclic normal subgroup of the fundamental group are either Seifert fibered or union of two twisted I-bundles along their boundary.
	www.math.tifr.res.in /~roushon/allahabad.html (189 words)

	Dehn Twists Have Linear Growth (ResearchIndex) (Site not responding. Last check: 2007-10-23)
		Yair N. Minsky June 20, 1997 In this note we give a simple proof that Dehn...
		The case of Dehn twists around a collection of disjoint curves is done in the same way; the case of an element h which is pseudo-Anosov or is reducible and has a power which is pseudo-Anosov on...
		1 A foliation of Teichmuller space by twist invariant disks (context) - Marden, Masur - 1975
	citeseer.ist.psu.edu /73703.html (355 words)

	CiteULike: Positive Dehn Twist Expressions for Some Elements of Finite Order (Site not responding. Last check: 2007-10-23)
		Positive Dehn Twist Expressions for Some Elements of Finite Order
		Note: You or your institution must have access rights to this article.
		@misc{citeulike:86813, abstract = {This paper was withdrawn by arXiv admin, as it was a duplicate of math/0501385.}, author = {Gurtas, Yusuf Z. citeulike-article-id = {86813}, eprint = {math.GT/0501384}, month = {January}, title = {Positive Dehn Twist Expressions for Some Elements of Finite Order}, url = {http://arxiv.org/abs/math.GT/0501384}, year = {2005} }
	www.citeulike.org /article/86813 (121 words)

	Twist Tie - Information (Site not responding. Last check: 2007-10-23)
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	www.freewebs.com /information24/twist-tie.html (311 words)

	Linear growth of infinite order mapping class group elements
		Fix a set of generators of the mapping class group of
		(the group is finitely generated; there are many proofs of this fact, already known to Dehn [
		The proof is based on the fact that given Dehn twist
	www.math.tifr.res.in /~pablo/teichmuller/node30.html (217 words)

	La page de Martin Lustig
		Krstic, M. Lustig et K. Vogtmann, An equivariant Whitehead algorithm and conjugacy for roots of Dehn twist automorphisms, Proc.
		Levitt et M. Lustig, Most automorphisms of a hyperbolic group have very simple dynamics, Ann.
		Cohen and M. Lustig,The conjugacy problem for Dehn twist automorphisms of free groups, Comment.
	junon.u-3mrs.fr /lustig (566 words)

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