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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Berry–Robbins problem</span></span>
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<p>In mathematics, the <b>Berry–Robbins problem</b> asks whether there is a continuous map from <a href="Configuration_(geometry)" title="Configuration (geometry)">configurations</a> of <i>n</i> points in <b>R</b><sup>3</sup> to the <a href="Flag_manifold" class="mw-redirect" title="Flag manifold">flag manifold</a> <i>U</i>(<i>n</i>)/<i>T</i><sup><i>n</i></sup> that is compatible with the <a href="Group_action_(mathematics)" class="mw-redirect" title="Group action (mathematics)">action</a> of the <a href="Symmetric_group" title="Symmetric group">symmetric group</a> on <i>n</i> points. It was posed by <a href="Michael_Berry_(physicist)" title="Michael Berry (physicist)">Berry</a> and Robbins in 1997,<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> and solved positively by <a href="Michael_Atiyah" title="Michael Atiyah">Atiyah</a> in 2000.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>
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<div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2></div>
<ul><li><a href="Atiyah_conjecture_on_configurations" title="Atiyah conjecture on configurations">Atiyah conjecture on configurations</a></li></ul>
<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>
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<li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">
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</style><cite id="CITEREFBerryRobbins1997" class="citation cs2"><a href="Michael_Berry_(physicist)" title="Michael Berry (physicist)">Berry, Michael V.</a>; Robbins, J. M. (1997), "Indistinguishability for quantum particles: spin, statistics and the geometric phase", <i>Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences</i>, <b>453</b> (1963): <span class="nowrap">1771–</span>1790, <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1997RSPSA.453.1771B">1997RSPSA.453.1771B</a>, <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frspa.1997.0096">10.1098/rspa.1997.0096</a>, <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0962-8444">0962-8444</a>, <a href="MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=1469170">1469170</a></cite></span>
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<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite id="CITEREFAtiyah2000" class="citation cs2"><a href="Michael_Atiyah" title="Michael Atiyah">Atiyah, Michael</a> (2000), "The geometry of classical particles", <i>Surveys in differential geometry</i>, Surv. Differ. Geom., VII, Int. Press, Somerville, MA, pp. <span class="nowrap">1–</span>15, <a href="MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=1919420">1919420</a></cite></span>
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<li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><cite id="CITEREFAtiyah2001" class="citation cs2"><a href="Michael_Atiyah" title="Michael Atiyah">Atiyah, Michael</a> (2001), "Configurations of points", <i>Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences</i>, <b>359</b> (1784): <span class="nowrap">1375–</span>1387, <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2001RSPTA.359.1375A">2001RSPTA.359.1375A</a>, <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frsta.2001.0840">10.1098/rsta.2001.0840</a>, <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1364-503X">1364-503X</a>, <a href="MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=1853626">1853626</a></cite></span>
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