David Baraglia

activity

20092026

most citedLeibniz algebroids, twistings and exceptional generalized geometry

78 citations · 426 across the 44 of their papers we have counts for

collaborators

50 papers

math.GT2026

Weights of finite cyclic actions on definite $4$ -manifolds

David Baraglia

Let $X$ be a closed, smooth, orientable, positive definite $4$ -manifold with $H_{1} (X; Z) = 0$ . Let $p$ be a prime and suppose that $G = Z_{p}$ acts smoothly on $X$ …

math.GT2026

Exotic diffeomorphisms of reducible $4$ -manifolds with odd $b_{+}$

David Baraglia

A diffeomorphism of a $4$ -manifold is said to be exotic if it is continuously isotopic to the identity but not smoothly isotopic to the identity. Ruberman constructed the first exa…

math.GT2026

Floer homotopy type and eta invariants of Seifert $3$ -manifolds fibering over $RP^{2}$

David Baraglia, Pedram Hekmati

We compute the Floer homology and Seiberg-Witten Floer homotopy type of Seifert rational homology $3$ -spheres which fiber over $RP^{2}$ . We show that they are all $L$ -spaces…

math.GT2025

Exotic diffeomorphisms of 4-manifolds with b_+ = 2

David Baraglia, Joshua Tomlin

Let $X$ be a compact, oriented, smooth, simply-connected $4$ -manifold. The mapping class group of $X$ is defined as the group of smooth isotopy classes of diffeomorphisms of $X$ . T…

math.KT2025

A Fourier-Mukai Transform For KR Theory

David Baraglia

In complex K-theory, the Fourier-Mukai transform is an isomorphism between K-theory groups of a torus and its dual torus which is defined by pullback, tensoring by the Poincaré lin…

math.GT2025

An adjunction inequality for Real embedded surfaces

David Baraglia

A Real structure on a $4$ -manifold $X$ is an orientation preserving smooth involution $σ$ . We say that an embedded surface $Σ \subset X$ is Real if $σ$ maps $Σ$ to itself orientatio…

math.GT2025

Exotic embedded surfaces and involutions from Real Seiberg-Witten theory

David Baraglia

Using Real Seiberg--Witten theory, Miyazawa introduced an invariant of certain 4-manifolds with involution and used this invariant to construct infinitely many exotic involutions o…

math.GT2024

Irreducible 4-manifolds can admit exotic diffeomorphisms

David Baraglia, Hokuto Konno

We prove that a variety of examples of minimal complex surfaces admit exotic diffeomorphisms, providing the first known instances of exotic diffeomorphisms of irreducible 4-manifol…

math.GT2024

Constraints on embedded spheres and real projective planes in 4-manifolds from Seiberg-Witten theory

David Baraglia

We calculate the Seiberg-Witten invariants of branched covers of prime degree, where the branch locus consists of embedded spheres. Aside from the formula itself, our calculations…

math.DG2024

Equivariant Seiberg-Witten theory

David Baraglia

We introduce and study equivariant Seiberg-Witten invariants for $4$ -manifolds equipped with a smooth action of a finite group $G$ . Our invariants come in two types: cohomological,…

math.GT2024

New invariants of involutions from Seiberg-Witten Floer theory

David Baraglia, Pedram Hekmati

We study equivariant Seiberg-Witten Floer theory of rational homology $3$ -spheres in the special case where the group action is given by an involution. The case of involutions dese…

math.GT2023★ 1 cited

On the mapping class groups of simply-connected smooth 4-manifolds

David Baraglia

The mapping class group $M (X)$ of a smooth manifold $X$ is the group of smooth isotopy classes of orientation preserving diffeomorphisms of $X$ . We prove a number of results about…

math.GT2023

The mod 2 Seiberg-Witten invariants of spin structures and spin families

David Baraglia

We completely determine the mod $2$ Seiberg-Witten invariants for any spin structure on any closed, oriented, smooth $4$ -manifold $X$ . Our computation confirms the validity of the…

math.GT2022★ 2 cited

Brieskorn spheres, cyclic group actions and the Milnor conjecture

David Baraglia, Pedram Hekmati

In this paper we further develop the theory of equivariant Seiberg-Witten-Floer cohomology of the two authors, with an emphasis on Brieskorn homology spheres. We obtain the followi…

math.GT2022★ 3 cited

Knot concordance invariants from Seiberg-Witten theory and slice genus bounds in 4-manifolds

David Baraglia

We construct a new family of knot concordance invariants $θ^{(q)} (K)$ , where $q$ is a prime number. Our invariants are obtained from the equivariant Seiberg-Witten-Floer cohomology…

math.GT2022★ 1 cited

On the slice genus of quasipositive knots in indefinite 4-manifolds

David Baraglia

Let $X$ be a closed indefinite $4$ -manifold with $b_{+} (X) = 3 (mod 4)$ and with non-vanishing mod $2$ Seiberg--Witten invariants. We prove a new lower bound on the genus…

math.GT2021★ 8 cited

Equivariant Seiberg-Witten-Floer cohomology

David Baraglia, Pedram Hekmati

We develop an equivariant version of Seiberg-Witten-Floer cohomology for finite group actions on rational homology $3$ -spheres. Our construction is based on an equivariant version…

math.DG2021★ 3 cited

Non-trivial smooth families of $K 3$ surfaces

David Baraglia

Let $X$ be a complex $K 3$ surface, $Diff (X)$ the group of diffeomorphisms of $X$ and $Diff_{0} (X)$ the identity component. We prove that the fundamental group of ${\rm Di…

math.DG2020★ 3 cited

Tautological classes of definite 4-manifolds

David Baraglia

We prove a diagonalisation theorem for the tautological, or generalised Miller-Morita-Mumford classes of compact, smooth, simply-connected definite $4$ -manifolds. Our result can be…

math.DG2020★ 3 cited

The alpha invariant of complete intersections

David Baraglia

We compute the alpha invariant of any smooth complex projective spin complete intersection of complex dimension $1 (mod 4)$ . We prove that the alpha invariant depends o…

math.DG2020★ 1 cited

An adjunction inequality obstruction to isotopy of embedded surfaces in 4-manifolds

David Baraglia

Consider a smooth $4$ -manifold $X$ and a diffeomorphism $f : X \to X$ . We give an obstruction in the form of an adjunction inequality for an embedded surface in $X$ to be isotopic…

math.DG2019★ 7 cited

A note on the Nielsen realization problem for K3 surfaces

David Baraglia, Hokuto Konno

We will show the following three theorems on the diffeomorphism and homeomorphism groups of a $K 3$ surface. The first theorem is that the natural map $π_{0}(Diff(K3)) \to Aut(H^{2}…

math.DG2019★ 18 cited

Constraints on families of smooth 4-manifolds from Bauer-Furuta invariants

David Baraglia

We obtain constraints on the topology of families of smooth $4$ -manifolds arising from a finite dimensional approximation of the families Seiberg-Witten monopole map. Amongst other…

math.DG2019★ 22 cited

On the Bauer-Furuta and Seiberg-Witten invariants of families of $4$ -manifolds

David Baraglia, Hokuto Konno

We show how the families Seiberg-Witten invariants of a family of smooth $4$ -manifolds can be recovered from the families Bauer-Furuta invariant via a cohomological formula. We use…

Weights of finite cyclic actions on definite 4-manifolds

Exotic diffeomorphisms of reducible 4-manifolds with odd b+​

Floer homotopy type and eta invariants of Seifert 3-manifolds fibering over RP2

Exotic diffeomorphisms of 4-manifolds with b_+ = 2

A Fourier-Mukai Transform For KR Theory

An adjunction inequality for Real embedded surfaces

Exotic embedded surfaces and involutions from Real Seiberg-Witten theory

Irreducible 4-manifolds can admit exotic diffeomorphisms

Constraints on embedded spheres and real projective planes in 4-manifolds from Seiberg-Witten theory

Equivariant Seiberg-Witten theory

New invariants of involutions from Seiberg-Witten Floer theory

On the mapping class groups of simply-connected smooth 4-manifolds

The mod 2 Seiberg-Witten invariants of spin structures and spin families

Brieskorn spheres, cyclic group actions and the Milnor conjecture

Knot concordance invariants from Seiberg-Witten theory and slice genus bounds in 4-manifolds

On the slice genus of quasipositive knots in indefinite 4-manifolds

Equivariant Seiberg-Witten-Floer cohomology

Non-trivial smooth families of K3 surfaces

Tautological classes of definite 4-manifolds

The alpha invariant of complete intersections

An adjunction inequality obstruction to isotopy of embedded surfaces in 4-manifolds

A note on the Nielsen realization problem for K3 surfaces

Constraints on families of smooth 4-manifolds from Bauer-Furuta invariants

On the Bauer-Furuta and Seiberg-Witten invariants of families of 4-manifolds

Weights of finite cyclic actions on definite $4$ -manifolds

Exotic diffeomorphisms of reducible $4$ -manifolds with odd $b_{+}$

Floer homotopy type and eta invariants of Seifert $3$ -manifolds fibering over $RP^{2}$

Non-trivial smooth families of $K 3$ surfaces

On the Bauer-Furuta and Seiberg-Witten invariants of families of $4$ -manifolds