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SUMMARY:Hông Vân Lê (Institute of Mathematics of ASCR)
DTSTART:20260318T123000Z
DTEND:20260318T133000Z
DTSTAMP:20260415T110957Z
UID:PHK-cohomology-seminar/151
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/PHK-cohomolo
 gy-seminar/151/">Minimal Unital Cyclic C∞-Algebras and the Real and Rati
 onal Homotopy Type of Closed Manifolds</a>\nby Hông Vân Lê (Institute o
 f Mathematics of ASCR) as part of Prague-Hradec Kralove seminar Cohomology
  in algebra\, geometry\, physics and statistics\n\nLecture held in blue le
 cture room + ZOOM meeting.\n\nAbstract\nUsing 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 grade
 d 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 generaliz
 ed 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 isot
 opy modulo (l − 2) of the corresponding minimal unital cyclic C∞ -alge
 bra 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)-conn
 ected closed manifold M of dimension 4r − 1 with b_r (M) ≤ 3 is intrin
 sically formal if there exists a φ ∈ H^(2r−1) (M\, R) such that the m
 ap 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 resul
 t\, showing that a (r − 1)-connected closed manifold M of dimension 4r w
 ith b_r (M) ≤ 2 is intrinsically formal under similar conditions. This t
 alk is based on \nhttps://arxiv.org/abs/2603.01219\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/151/
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