Periodic Floer pro-spectra from the Seiberg-Witten equations

Peter B. Kronheimer; Ciprian Manolescu

Home/Archive/arXiv

arXiv · math/0203243

Periodic Floer pro-spectra from the Seiberg-Witten equations

Peter B. Kronheimer·Ciprian Manolescu

View original source ↗Read source document ↗Export metadata ↓

Abstract

Given a three-manifold with b_1=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 pro-spectra. Various functors applied to these invariants give different flavors of Seiberg-Witten Floer homology. We also construct stable homotopy versions of the relative Seiberg-Witten invariants for certain four-manifolds with boundary.

Explore related subjects

math.GT math.DG

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Peter B. Kronheimer, Ciprian Manolescu. 2014-02-03. Periodic Floer pro-spectra from the Seiberg-Witten equations. https://arxiv.org/abs/math/0203243

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Relationship between quandle shadow cocycle invariants and Vassiliev invariants

As one of the problems in his list [20], T. Ohtsuki proposed to study relations between quandle cocycle invariants and quantum invariants. The aim of this paper is to answer one of those questions. We prove that the coefficient of the finite perturbative expansion of the quandle shadow cocycle invariant defined by $(\Z /p\Z)$-Laurent polynomial quandle is Vassiliev invariant for any braids.

math.GT↗

arXiv2026

Holed cone structures on 3-manifolds

We introduce holed cone structures on 3-manifolds to generalize cone structures. In the same way as a cone structure, a holed cone structure induces the holonomy representation. We consider the deformation space consisting of the holed cone structures on a 3-manifold whose holonomy representations are irreducible. This deformation space for positive cone angles is a covering space on a reasonable subspace of the character variety.

math.GT↗

arXiv2026

Zariski dense hyperbolic 3-manifold groups in $\mathrm{SL}(4,\mathbb{Z})$

We show that $\mathrm{SL}(4,\mathbb{Z})$ contains an infinite family of Zariski-dense subgroups isomorphic to the fundamental group of a fixed closed hyperbolic $3$-manifold, which are pairwise noncommensurable up to conjugacy.

math.GT↗