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

[Petr Somberg]

 This is a gentle reminder of our seminar.

--------------------------------------------------------------------------


     Cohomology in algebra, geometry, physics and statistics




         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


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





          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





 _______________________________________________
phk_seminar mailing list
phk_seminar at math.cas.cz
https://list.math.cas.cz/listinfo/phk_seminar