# Seiberg-Witten-Floer stable homotopy type of three-manifolds with b_1=0

@article{Manolescu2001SeibergWittenFloerSH, title={Seiberg-Witten-Floer stable homotopy type of three-manifolds with b\_1=0}, author={Ciprian Manolescu}, journal={arXiv: Differential Geometry}, year={2001} }

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 delicate transversality problems in the standard approach. We also define a relative invariant of four-manifolds with boundary which generalizes the Bauer-Furuta stable homotopy… Expand

#### 76 Citations

PERIODIC FLOER PRO-SPECTRA FROM THE SEIBERG-WITTEN EQUATIONS

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Given a three-manifold with b1 = 1 and a nontorsion spin c structure, we use finite dimensional approximation to construct from the Seiberg-Witten equations two invariants in the form of a periodic… Expand

Pin(2)-equivariant Seiberg-Witten Floer homology and the Triangulation Conjecture

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We define Pin(2)-equivariant Seiberg-Witten Floer homology for rational homology 3-spheres equipped with a spin structure. The analogue of Froyshov's correction term in this setting is an… Expand

Gluing formula for the stable cohomotopy version of Seiberg-Witten invariants along 3-manifolds with $b_1 > 0$

- Mathematics
- 2014

We will define a version of Seiberg-Witten-Floer stable ho- motopy types for a closed, oriented 3-manifold Y with b1(Y ) > 0 and a spin-c structure c on Y with c1(c) torsion under an assumption on Y.… Expand

Equivariant Seiberg-Witten-Floer cohomology

- Mathematics
- 2021

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 of the… Expand

Twisted Manolescu-Floer spectra for Seiberg-Witten monopoles

- Mathematics
- 2013

In this thesis, we extend Manolescus and
Kronheimer-Manolescus construction of Floer homotopy type to
general 3-manifolds. This Floer homotopy type is a candidate for an
object whose suitable… Expand

A gluing theorem for the relative Bauer-Furuta invariants

- Mathematics
- 2003

In a previous paper we have constructed an invariant of fourdimensional manifolds with boundary in the form of an element in the stable homotopy group of the Seiberg-Witten Floer spectrum of the… Expand

On the intersection forms of spin four-manifolds with boundary

- Mathematics
- 2013

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… Expand

Positive scalar curvature and homology cobordism invariants

- Mathematics
- 2021

We determine the local equivalence class of the Seiberg–Witten Floer stable homotopy type of a spin rational homology 3-sphere Y embedded into a spin rational homology S × S with a positive scalar… Expand

AND CIPRIAN MANOLESCU in the sense

- 2014

Given a three-manifold with b1 = 1 and a nontorsion spin c structure, we use finite dimensional approximation to construct from the Seiberg-Witten equations two invariants in the form of a periodic… Expand

Unfolded Seiberg-Witten Floer spectra, II: Relative invariants and the gluing theorem

- Mathematics
- 2018

We use the construction of unfolded Seiberg-Witten Floer spectra of general 3-manifolds defined in our previous paper to extend the notion of relative Bauer-Furuta invariants to general 4-manifolds… Expand

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