B. Botvinnik

activity

19992026

most citedInfinite loop spaces and positive scalar curvature

56 citations · 146 across the 34 of their papers we have counts for

collaborators

35 papers

math.GT2026

Brunnian links and Kontsevich graph complex I

Boris Botvinnik, Tadayuki Watanabe

We construct a natural chain map from the Kontsevich graph complex to the rational singular chain complex of $B Diff_{\partial} (D^{2 k})$ when the dimension $2 k$ is sufficient…

math.DG2025

Classification of spin $^{c}$ manifolds with generalized positive scalar curvature

Boris Botvinnik, Paolo Piazza, Jonathan Rosenberg

Suppose $M$ is a closed $n$ -dimensional spin $^{c}$ manifold with spin $^{c}$ structure $σ$ and associated spin $^{c}$ line bundle $L$ . If one fixes a Riemannian metric $g$ on $M$ and a con…

math.DG2024

On the topology of the moduli space of positive scalar curvature concordances

Boris Botvinnik, David J. Wraith

Let $M$ be a manifold which admits a metric with positive scalar curvature (or a positive intermediate curvature in a suitable sense). We study the moduli space ${\mathscr{M}}^{\ma…

math.DG2024

Generalized positive scalar curvature on spin $^{c}$ manifolds

Boris Botvinnik, Jonathan Rosenberg

Let $(M, L)$ be a (compact) non-spin spin $^{c}$ manifold. Fix a Riemannian metric $g$ on $M$ and a connection $A$ on $L$ , and let $D_{L}$ be the associated spin $^{c}$ Dirac operator. Let…

math.AT2023

Symmetries of exotic spheres via complex and quaternionic Mahowald invariants

Boris Botvinnik, J. D. Quigley

We use new homotopy-theoretic tools to prove the existence of smooth $U (1)$ - and $S p (1)$ -actions on infinite families of exotic spheres. Such families of spheres are propagated by…

math.GT2022★ 1 cited

Families of diffeomorphisms and concordances detected by trivalent graphs