A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Invariants for connected sums of 3-manifolds, proving Furuta's theorem.
Authors prove existence of exotic surfaces and invariants not detecting self-diffeomorphisms.
S.Bauer and M.Furuta defined a stable cohomotopy refinement of the Seiberg-Witten invariants. In this paper, we prove a vanishing theorem of Bauer-Furuta invariants for 4-manifolds with smooth Z/2-actions. As an application, we give a constraint on smooth Z/2-actions on homotopy K3#K3, and construct a nonsmoothable loc…
The paper constrains families of smooth 4-manifolds using Seiberg-Witten invariants.
New examples of 3-manifolds not obtained by surgery on knots.
Furuta's ``10/8-th's'' theorem gives a bound on the magnitude of the signature of a smooth spin 4-manifold in terms of the second Betti number. We show that in the presence of a Z/2^p action, his bound can be strengthened. As applications, we give new genus bounds on classes with divisibility and we give a classificati…
Using Seiberg-Witten Floer spectrum and Pin(2)-equivariant KO-theory, we prove new Furuta-type inequalities on the intersection forms of spin cobordisms between homology -spheres. As an application, we give explicit constrains on the intersection forms of spin -manifolds bounded by Brieskorn spheres $\pmΣ(2,3,6k\…
This is the second in a series of papers studying the relationship between Rohlin's theorem and gauge theory. We discuss an invariant of a homology S^1 cross S^3 defined by Furuta and Ohta as an analogue of Casson's invariant for homology 3-spheres. Our main result is a calculation of the Furuta-Ohta invariant for the …
Study of Bauer-Furuta invariants under Lie group actions and Galois coverings.
In a previous paper we have constructed an invariant of four-dimensional manifolds with boundary in the form of an element in the stable homotopy group of the Seiberg-Witten Floer spectrum of the boundary. Here we prove that when one glues two four-manifolds along their boundaries, the Bauer-Furuta invariant of the res…
Study on constraints for topological and smooth realizations of line arrangements and configurations.
Extends invariants to 4-manifolds with boundary.
Study BF invariants using simple type concepts.
Established a stable cohomotopy refinement for Pin(2) monopole invariants.
Novel construction of Bauer--Furuta invariant using sheaves of spectra.
New inequality for links in 3D using 4D invariants.
Proves a formula for a special invariant of 4-manifolds.
Proved boundary Dehn twist is exotic for Milnor fibers with specific conditions.
New slicing obstruction from knot surgery yields non-trivial results.
New knots have unique Whitehead doubles.
New spectral construction for 3-manifolds with non-zero first Betti number.
In this paper, we study Manolescu's construction of the relative Bauer-Furuta invariants arising from the Seiberg-Witten equations on 4-manifolds with boundary. The main goal is to introduce a new gauge fixing condition in order to apply the finite dimensional approximation technique. We also hope to provide a framewor…
Researchers found nonsmoothable actions of Z2 * Z2 on spin 4-manifolds.
Study Lefschetz fibrations with 4D fibers using Seiberg-Witten theory.
We introduce a variant of the Seiberg-Witten equations, Pin^-(2)-monopole equations, and give its applications to intersection forms with local coefficients of 4-manifolds. The first application is an analogue of Froyshov's results on 4-manifolds which have definite forms with local coefficients. The second is a local …
Refines Kronheimer-Mrowka's invariant for 4-manifolds with specific boundary conditions.
Formulae prove equivalence of two invariants on specific 4-manifolds.
Using Furuta's idea of finite dimensional approximation in Seiberg-Witten theory, we refine Seiberg-Witten Floer homology to obtain an invariant of homology 3-spheres which lives in the S^1-equivariant graded suspension category. In particular, this gives a construction of Seiberg-Witten Floer homology that avoids the …
The main theorem describes the behaviour of the stable cohomotopy invariant defined in the first article (joint with M. Furuta) in this series of two under the operation of taking connected sums of four-manifolds: The invariant of a connected sum is the smash product (in the sense of equivariant spectra) of the invaria…
The study explores stable diffeomorphism groups in 4-manifolds using localisation and invariants.
We use Furuta's result, usually referred to as ``10/8-conjecture'', to show that for any compact 3-manifold the open manifold $M\times\r$ has infinitely many different smooth structures. Another consequence of Furuta's result is existence of infinitely many smooth structures on open topological 4-manifolds with a t…
Study cohomotopy classes for 4-manifolds using complex spin structures.
This is an expository article on the equivariant local index developed by Fujita, Furuta, and the author in arXiv:1008.5007.
The paper provides a new inequality for 4-manifolds and uses it to study knot sliceness and symplectic embeddings.
Diagonalizes tautological classes of definite 4-manifolds.
This paper constructs exotic diffeomorphisms on reducible 4-manifolds with odd b+.
Paper solves a 4D topology problem using Pin(2)-equivariant Mahowald invariants.
New geometric interpretation of a group class using circle action and rotation numbers.
New formula connects Bauer-Furuta and Seiberg-Witten invariants of families of 4-manifolds.
Paper optimizes energy-based controller for swinging up a pendulum using entropy search.
New invariant shows Dehn twist on connected sum of homology tori is not isotopic to identity.
Starting from ideas of Furuta, we develop a general formalism for the construction of cohomotopy invariants associated with a certain class of -equivariant non-linear maps between Hilbert bundles. Applied to the Seiberg-Witten map, this formalism yields a new class of cohomotopy Seiberg-Witten invariants which hav…
The purpose of these notes is to show that the methods introduced by Bauer and Furuta in order to refine the Seiberg-Witten invariants of smooth 4-dimensional manifolds can also be used to obtain stable homotopy classes from Riemann surfaces, using the vortex equations on the latter.
We consider several differential-topological invariants of compact 4-manifolds which directly arise from Riemannian variational problems. Using recent results of Bauer and Furuta, we compute these invariants in many cases that were previously intractable. In particular, we are now able to calculate the Yamabe invariant…
The main goal of this article is to obtain a condition under which an infinite collection of satellite knots (with companion a positive torus knot and pattern similar to the Whitehead link) freely generates a subgroup of infinite rank in the smooth concordance group. This goal is attained by examining bot…
We prove Furuta-type bounds for the intersection forms of spin cobordisms between homology 3-spheres. The bounds are in terms of a new numerical invariant of homology spheres, obtained from Pin(2)-equivariant Seiberg-Witten Floer K-theory. In the process we introduce the notion of a Floer K_G-split homology sphere; thi…
This is a survey of our recent work with Tom Mrowka on Seiberg-Witten gauge theory and index theory for manifolds with periodic ends. We explain how this work leads to a new invariant, which is related to the classical Rohlin invariant of homology 3-spheres and to the Furuta-Ohta invariant originating in Yang-Mills gau…
New invariant connects symplectic fillings and contact structures.