[PHK_seminar] [Cohomology]Wednesday 18 Mar, Hông Vân Lê

[Igor Khavkine]

Dear All,

The video recording of the talk by Hông Vân Lê from this week is now 
available on YouTube at

   https://youtu.be/bFSS4p9genI

The slides are available from

   https://users.math.cas.cz/~hvle/PHK/LeCinfty2026.pdf

Both links have also been recorded at the ResearchSeminars announcement

   https://researchseminars.org/talk/PHK-cohomology-seminar/151/

Best,

Igor

On 3/16/26 1:00 PM, sender of seminar announcement via phk_seminar wrote:
> Wednesday, 18 March 2026 - 13:30 to 14:30
> Place: Institute of Mathematics of ASCR, Žitná 25, Praha 1, the blue 
> lecture room + ZOOM meeting
> 
> Speaker: Hông Vân Lê, Institute of Mathematics of ASCR
> Title: Minimal Unital Cyclic C∞ -Algebras and the Real and Rational 
> Homotopy Type of Closed Manifolds
> 
> Abstract
> 
> 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
> 
> enhancements of a finite-type graded commutative algebra $H^*$. We 
> determine obstruction classes defining the extendability of isotopy
> 
> modulo $k$ to isotopy modulo $(k+1)$ for minimal $C_\infty$-algebra 
> enhancements of $H^*$ and demonstrate their generalized additivity.
> 
> 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
> 
> 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
> 
> the cohomology algebra H*(M, F) and the isotopy modulo (l − 2) of the 
> corresponding minimal unital cyclic C∞ -algebra
> 
> enhancements of H*(M, F) for F = R, Q, respectively. Combining this with 
> the Hodge homotopy introduced by Fiorenza-Kawai-Lê-Schwachhöfer ,
> 
> 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
> 
> 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.
> 
> Furthermore, we provide a new proof and extension of Cavalcanti’s 
> result, showing that a (r − 1)-connected closed manifold M of dimension
> 
> 4r with br (M ) ≤ 2 is intrinsically formal under similar conditions. 
> This talk is based on https://arxiv.org/abs/2603.01219 .
> 
> ----------------------------------------------------
> 
> We shall open the seminar room and ZOOM meeting at 13.15 for (virtual) 
> coffee and close ZOOM at 15.00
> 
> 
> Join Zoom Meeting
> 
> 
> https://cesnet.zoom.us/j/99598413922? 
> pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09 <https://cesnet.zoom.us/ 
> j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09>
> 
> 
> Meeting ID:99598413922
> 
> Passcode:Galois
> 
> ------------------------------------------------------------------------------------------------
> 
> On Wednesday 25 March Aaron Kettner shall give a talk on $K$-theory for 
> the $C^*$-algebra of a homeomorphism and a vector bundle <https:// 
> www.math.cas.cz/index.php/events/event/4131>
> 
> For more information see the seminar web page at
> https://www.math.cas.cz/index.php/events/seminar/16
> 
> Cohomology in algebra, geometry, physics and statistics mailing list
> phk_seminar at math.cas.cz
> https://list.math.cas.cz/listinfo/phk_seminar@math.cas.cz
> 
> 
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