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<title>Cohomology in algebra, geometry, physics and statistics</title>
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Wednesday, 29 October 2025 - 13:30 to 14:30 <br />
Place: Institute of Mathematics of ASCR, Žitná 25, Praha 1, ZOOM meeting
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Speaker: Anton Galaev, Hradec-Kralove University<br />
Title: Holonomy of K-contact sub-Riemannian manifolds
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Abstract <br />
<p><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);" class="ql-font-monospace">Given a contact sub-Riemannian manifold (M, θ, g), where θ is a contact form on M, and g is a metric on the contact distribution</span></p><p><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);" class="ql-font-monospace"> D = ker θ, there is the Schouten connection, which defines parallel transport of vectors tangent to D along curves tangent to D. </span></p><p><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);" class="ql-font-monospace">The holonomy group of this connection is called the horizontal holonomy group. The adapted connection is an extension of the </span></p><p><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);" class="ql-font-monospace">horizontal connection to a connection on the vector bundle D over M. I will show that in the K-contact case (which means that the</span></p><p><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);" class="ql-font-monospace">Reeb vector field is a Killing one), the holonomy of the adapted connection is the holonomy of some Riemannian manifold, and the </span></p><p><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);" class="ql-font-monospace">horizontal holonomy either coincides with the holonomy of the adapted connection, or it is a codimension-one normal subgroup of </span></p><p><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);" class="ql-font-monospace"><span class="ql-cursor"></span>the later group. I will discuss the question of existence of parallel horizontal spinors, examples, and consequences.</span></p><p class="ql-align-justify"><span style="background-color: rgb(255, 255, 255); color: rgb(34, 34, 34);">----------------------------------------------------------</span></p><p class="ql-align-justify"><br></p><p class="ql-align-justify"><span style="background-color: rgb(255, 255, 255); color: rgb(34, 34, 34);">We shall open ZOOM meeting at 13.15 for virtual coffee and close ZOOM at 15.00</span></p><p class="ql-align-justify"><br></p><p class="ql-align-justify"><span style="background-color: rgb(255, 255, 255); color: rgb(34, 34, 34);">Join Zoom Meeting</span></p><p class="ql-align-justify"><br></p><p class="ql-align-justify"><a href="https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09" rel="noopener noreferrer" target="_blank" style="color: rgb(17, 85, 204); background-color: rgb(255, 255, 255);">https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09</a></p><p class="ql-align-justify"><br></p><p class="ql-align-justify"><span style="background-color: rgb(255, 255, 255); color: rgb(34, 34, 34);">Meeting ID:99598413922</span></p><p class="ql-align-justify"><span style="background-color: rgb(255, 255, 255); color: rgb(34, 34, 34);">Passcode:Galois</span></p><p class="ql-align-justify"><br></p><p class="ql-align-justify"><span style="background-color: rgb(255, 255, 255); color: rgb(34, 34, 34);">---------------------------------------------------------------------------------------------------------------</span></p><p><span style="background-color: rgb(255, 255, 255); color: rgb(34, 34, 34);">On Wednesday November 5 our seminar shall start at 4 PM. Professor Ida Zadeh shall give a lecture </span></p><p><span style="background-color: rgb(255, 255, 255); color: rgb(34, 34, 34);">``</span>Tracking the symmetries of Z3-orbifold K3s within the Mathieu groups".</p><p class="ql-align-justify"><br></p><p class="ql-align-justify"><br></p><p class="ql-align-justify"><span style="background-color: rgb(255, 255, 255); color: rgb(34, 34, 34);"> For more information, see the seminar web page at</span></p><p class="ql-align-justify">https://www.math.cas.cz/index.php/events/seminar/16</p><p><br></p><p><br></p>
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For more information see the seminar web page at <br />
https://www.math.cas.cz/index.php/events/seminar/16
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Cohomology in algebra, geometry, physics and statistics mailing list <br />
phk_seminar@math.cas.cz <br />
https://list.math.cas.cz/listinfo/phk_seminar@math.cas.cz
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