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<meta content="Easdown, David" name="eprints.creators_name" />
<meta content="East, James" name="eprints.creators_name" />
<meta content="FitzGerald, D.G." name="eprints.creators_name" />
<meta content="de@maths.usyd.edu.au" name="eprints.creators_id" />
<meta content="James.East@latrobe.edu.au" name="eprints.creators_id" />
<meta content="D.FitzGerald@utas.edu.au" name="eprints.creators_id" />
<meta content="Araujo, Isabel M" name="eprints.editors_name" />
<meta content="Branco, Mario J J" name="eprints.editors_name" />
<meta content="Fernandes, Vitor H" name="eprints.editors_name" />
<meta content="Gomes, Gracinda M S" name="eprints.editors_name" />
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<meta content="What is the untangling effect on a braid if one is allowed to snip a string, or if two specified strings are allowed to pass through each other, or even allowed to merge and part as newly reconstituted strings? To calculate the effects, one works in an appropriate factorizable inverse
monoid, some aspects of a general theory of which are discussed in this
paper. The coset monoid of a group arises, and turns out to have a universal
property within a certain class of factorizable inverse monoids. This theory
is dual to the classical construction of fundamental inverse semigroups from
semilattices. In our braid examples, we will focus mainly on the ``merge and
part'' alternative, and introduce a monoid which is a natural preimage of
the largest factorizable inverse submonoid of the dual symmetric inverse
monoid on a finite set, and prove that it embeds in the coset monoid of the
braid group." name="eprints.abstract" />
<meta content="2004" name="eprints.date" />
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<meta content="[1] J. Baez, Link invariants of finite type and perturbation theory, Lett.
Math. Phys. 26 (1992), 43-51. 80 (1973), 48-52.
[2] Joan S. Birman, New points of view in knot theory, Bull. Amer. Math.
Soc., 28 (1993), 253-287.
[3] D. Easdown and T.G. Lavers, The inverse braid monoid, Advances in
Mathematics, to appear.
[4] James East, The factorisable braid monoid, in preparation.
[5] D.G. FitzGerald and Jonathan Leech, Dual symmetric inverse monoids
and representation theory, J. Austral. Math. Soc., 64 (1998), 345-367.
[6] Jonathan Leech, Inverse monoids with a natural semilattice ordering, Proc. London Math. Soc. 70 (1995), 146-182.
[7] D.B. McAlister, Embedding inverse semigroups in coset semigroups,
Semigroup Forum 20 (1980), 255-267.
[8] W.D. Munn, Uniform semilattices and bisimple inverse semigroups,
Quart. J. Math. Oxford (2) 17 (1966), 151-159.
[9] K.S.S. Nambooripad and R. Veeramony, Subdirect products of regular
semigroups, Semigroup Forum 27 (1983), 265-307.
[10] B.M. Schein, Semigroups of strong subsets, Volzhsky Matematichesky
Sbornik 4 (1966), 180-186.
[11] B.M. Schein, Cosets in groups and semigroups, Semigroups with applications,
eds. Howie, Munn, Weinert, World Scientific, Singapore 1992,
205-221. 4 (1966), 180-186." name="eprints.referencetext" />
<meta content="Easdown, David and East, James and FitzGerald, D.G. (2004) Braids and factorizable inverse monoids. In: Semigroups and languages: Proceedings of the Workshop Semigroups and Languages, Lisboa, Portugal, 27 - 29 November 2002. . World Scientific Press, pp. 86-105." name="eprints.citation" />
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<meta content="What is the untangling effect on a braid if one is allowed to snip a string, or if two specified strings are allowed to pass through each other, or even allowed to merge and part as newly reconstituted strings? To calculate the effects, one works in an appropriate factorizable inverse
monoid, some aspects of a general theory of which are discussed in this
paper. The coset monoid of a group arises, and turns out to have a universal
property within a certain class of factorizable inverse monoids. This theory
is dual to the classical construction of fundamental inverse semigroups from
semilattices. In our braid examples, we will focus mainly on the ``merge and
part'' alternative, and introduce a monoid which is a natural preimage of
the largest factorizable inverse submonoid of the dual symmetric inverse
monoid on a finite set, and prove that it embeds in the coset monoid of the
braid group." name="DC.description" />
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<h1 class="ep_tm_pagetitle">Braids and factorizable inverse monoids</h1>
<p style="margin-bottom: 1em" class="not_ep_block"><span class="person_name">Easdown, David</span> and <span class="person_name">East, James</span> and <span class="person_name">FitzGerald, D.G.</span> (2004) <xhtml:em>Braids and factorizable inverse monoids.</xhtml:em> In: Semigroups and languages: Proceedings of the Workshop Semigroups and Languages, Lisboa, Portugal, 27 - 29 November 2002. . World Scientific Press, pp. 86-105.</p><p style="margin-bottom: 1em" class="not_ep_block"></p><table style="margin-bottom: 1em" class="not_ep_block"><tr><td valign="top" style="text-align:center"><a onmouseover="EPJS_ShowPreview( event, 'doc_preview_1813' );" href="http://eprints.utas.edu.au/1412/1/eef_fim2_v07.pdf" onmouseout="EPJS_HidePreview( event, 'doc_preview_1813' );"><img alt="[img]" src="http://eprints.utas.edu.au/style/images/fileicons/application_pdf.png" class="ep_doc_icon" border="0" /></a><div class="ep_preview" id="doc_preview_1813"><table><tr><td><img alt="" src="http://eprints.utas.edu.au/1412/thumbnails/1/preview.png" class="ep_preview_image" border="0" /><div class="ep_preview_title">Preview</div></td></tr></table></div></td><td valign="top"><a href="http://eprints.utas.edu.au/1412/1/eef_fim2_v07.pdf"><span class="ep_document_citation">PDF</span></a> - Requires a PDF viewer<br />156Kb</td></tr></table><p style="margin-bottom: 1em" class="not_ep_block">Official URL: <a href="http://eproceedings.worldscinet.com/9789812702616/9789812702616.shtml">http://eproceedings.worldscinet.com/9789812702616/9789812702616.shtml</a></p><div class="not_ep_block"><h2>Abstract</h2><p style="padding-bottom: 16px; text-align: left; margin: 1em auto 0em auto">What is the untangling effect on a braid if one is allowed to snip a string, or if two specified strings are allowed to pass through each other, or even allowed to merge and part as newly reconstituted strings? To calculate the effects, one works in an appropriate factorizable inverse
monoid, some aspects of a general theory of which are discussed in this
paper. The coset monoid of a group arises, and turns out to have a universal
property within a certain class of factorizable inverse monoids. This theory
is dual to the classical construction of fundamental inverse semigroups from
semilattices. In our braid examples, we will focus mainly on the ``merge and
part'' alternative, and introduce a monoid which is a natural preimage of
the largest factorizable inverse submonoid of the dual symmetric inverse
monoid on a finite set, and prove that it embeds in the coset monoid of the
braid group.</p></div><table style="margin-bottom: 1em" cellpadding="3" class="not_ep_block" border="0"><tr><th valign="top" class="ep_row">Item Type:</th><td valign="top" class="ep_row">Book Chapter</td></tr><tr><th valign="top" class="ep_row">Keywords:</th><td valign="top" class="ep_row">factorizable inverse monoid, merge and part monoid, coset monoid</td></tr><tr><th valign="top" class="ep_row">Subjects:</th><td valign="top" class="ep_row"><a href="http://eprints.utas.edu.au/view/subjects/230105.html">230000 Mathematical Sciences > 230100 Mathematics > 230105 Group Theory And Generalisations (Incl. Topological Groups And Lie Groups)</a></td></tr><tr><th valign="top" class="ep_row">ID Code:</th><td valign="top" class="ep_row">1412</td></tr><tr><th valign="top" class="ep_row">Deposited By:</th><td valign="top" class="ep_row"><span class="ep_name_citation"><span class="person_name">Dr D. G. FitzGerald</span></span></td></tr><tr><th valign="top" class="ep_row">Deposited On:</th><td valign="top" class="ep_row">19 Jul 2007</td></tr><tr><th valign="top" class="ep_row">Last Modified:</th><td valign="top" class="ep_row">09 Jan 2008 02:30</td></tr><tr><th valign="top" class="ep_row">ePrint Statistics:</th><td valign="top" class="ep_row"><a target="ePrintStats" href="/es/index.php?action=show_detail_eprint;id=1412;">View statistics for this ePrint</a></td></tr></table><p align="right">Repository Staff Only: <a href="http://eprints.utas.edu.au/cgi/users/home?screen=EPrint::View&eprintid=1412">item control page</a></p>
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