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<title>Cohomology in algebra, geometry, physics and statistics</title>
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Wednesday, 18 March 2026 - 13:30 to 14:30 <br />
Place: Institute of Mathematics of ASCR, Žitná 25, Praha 1, the blue lecture room + ZOOM meeting
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Speaker: Hông Vân Lê, Institute of Mathematics of ASCR<br />
Title: Minimal Unital Cyclic C∞ -Algebras and the Real and Rational Homotopy Type of Closed Manifolds
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Abstract <br />
<p>Using the notion of isotopy modulo $k$, with $k \in \mathbb{N}^+$, we introduce a stratification on the set of all minimal $C_\infty$-algebra </p><p>enhancements of a finite-type graded commutative algebra $H^*$. We determine obstruction classes defining the extendability of isotopy </p><p>modulo $k$ to isotopy modulo $(k+1)$ for minimal $C_\infty$-algebra enhancements of $H^*$ and demonstrate their generalized additivity. </p><p>As a result, we define a complete set of invariants of the rational homotopy type of closed simply connected manifolds M . We prove that if </p><p>M is a closed (r − 1)-connected manifold of dimension n ≤ l(r − 1) + 2 (where r ≥ 2, l ≥ 4), the real and rational homotopy type of M is defined uniquely by </p><p>the cohomology algebra H*(M, F) and the isotopy modulo (l − 2) of the corresponding minimal unital cyclic C∞ -algebra</p><p>enhancements of H*(M, F) for F = R, Q, respectively. Combining this with the Hodge homotopy introduced by Fiorenza-Kawai-Lê-Schwachhöfer , </p><p>we provide a new proof of a theorem by Crowley-Nordström: a (r −1)-connected closed manifold M of dimension 4r − 1 with br (M ) ≤ 3 is </p><p>intrinsically formal if there exists a φ ∈ H^ {2r−1} (M, R) such that the map H^r (M, R) → H^ {3r−1} (M, R), x → φ ∪ x is an isomorphism.</p><p>Furthermore, we provide a new proof and extension of Cavalcanti’s result, showing that a (r − 1)-connected closed manifold M of dimension</p><p>4r with br (M ) ≤ 2 is intrinsically formal under similar conditions. This talk is based on https://arxiv.org/abs/2603.01219 .</p><p><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);" class="ql-font-monospace">----------------------------------------------------</span></p><p class="ql-align-justify"><span style="background-color: rgb(255, 255, 255); color: rgb(34, 34, 34);">We shall open the seminar room and 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>------------------------------------------------------------------------------------------------</p><p>On Wednesday 25 March Aaron Kettner shall give a talk on <a href="https://www.math.cas.cz/index.php/events/event/4131" rel="noopener noreferrer" target="_blank">$K$-theory for the $C^*$-algebra of a homeomorphism and a vector bundle </a></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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