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

Manolescu, Ciprian

doi:10.1090/jams829

Cited by 116 publications

(241 citation statements)

References 54 publications

(168 reference statements)

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“…Let

G = Pin (2)

be the group consisting of two copies of the complex unit circle, along with a map

j

interchanging them, so that

i j = - j i

and

j^{2} = - 1

. In , Manolescu associated to a spin three‐manifold

(Y, s)

the

G

‐equivariant Seiberg–Witten Floer homology

{italicSWFH}^{G} false(Y, frakturs false)

, which is the Borel homology of a stable homotopy type

SWF (Y, s)

. From its module structure, he defined homology cobordism invariants

α, β, γ

as analogues of the Frøyshov invariant of the usual,

S^{1}

‐equivariant, Seiberg–Witten Floer homology .…”

Section: Introductionmentioning

confidence: 99%

Manolescu invariants of connected sums

Stoffregen

2017

Proc. London Math. Soc.

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Abstract. We give inequalities for the Manolescu invariants α, β, γ under the connected sum operation. We compute the Manolescu invariants of connected sums of some Seifert fiber spaces. Using these same invariants, we provide a proof of Furuta's Theorem, the existence of a Z 8 subgroup of the homology cobordism group. To our knowledge, this is the first proof of Furuta's Theorem using monopoles. We also provide information about Manolescu invariants of the connected sum of n copies of a three-manifold Y , for large n.

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“…Let

G = Pin (2)

be the group consisting of two copies of the complex unit circle, along with a map

j

interchanging them, so that

i j = - j i

and

j^{2} = - 1

. In , Manolescu associated to a spin three‐manifold

(Y, s)

the

G

‐equivariant Seiberg–Witten Floer homology

{italicSWFH}^{G} false(Y, frakturs false)

, which is the Borel homology of a stable homotopy type

SWF (Y, s)

. From its module structure, he defined homology cobordism invariants

α, β, γ

as analogues of the Frøyshov invariant of the usual,

S^{1}

‐equivariant, Seiberg–Witten Floer homology .…”

Section: Introductionmentioning

confidence: 99%

Manolescu invariants of connected sums

Stoffregen

2017

Proc. London Math. Soc.

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show abstract

“…where η I µ , complexified four-vectors, which take the following form: 25) and τ = C 0 + ie −φ denotes the complexified string coupling of Type IIB string theory. This structure results in the discrete gauge invariance of the effective four-dimensional action, which corresponds to the Heisenberg discrete symmetry specified by k 1 , k 2 , k 3 and M .…”

Section: Jhep07(2017)129mentioning

confidence: 99%

Type II string theory on Calabi-Yau manifolds with torsion and non-Abelian discrete gauge symmetries

Braun¹,

Cvetič

Donagi

et al. 2017

J. High Energ. Phys.

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Abstract:We provide the first explicit example of Type IIB string theory compactification on a globally defined Calabi-Yau threefold with torsion which results in a fourdimensional effective theory with a non-Abelian discrete gauge symmetry. Our example is based on a particular Calabi-Yau manifold, the quotient of a product of three elliptic curves by a fixed point free action of Z 2 × Z 2 . Its cohomology contains torsion classes in various degrees. The main technical novelty is in determining the multiplicative structure of the (torsion part of) the cohomology ring, and in particular showing that the cup product of second cohomology torsion elements goes non-trivially to the fourth cohomology. This specifies a non-Abelian, Heisenberg-type discrete symmetry group of the four-dimensional theory.

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“…For higher dimensions including the 4-dimensional spacetime, a triangulation does not necessarily exist and if it exists it is not guaranteed to be unique or to correspond to a single space [90][91][92][93].…”

Section: Chaptermentioning

confidence: 99%

The Universal Coefficient Theorem and Quantum Field Theory

Patrascu

2017

Springer Theses

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

Cited by 116 publications

References 54 publications

Manolescu invariants of connected sums

Manolescu invariants of connected sums

Type II string theory on Calabi-Yau manifolds with torsion and non-Abelian discrete gauge symmetries

The Universal Coefficient Theorem and Quantum Field Theory

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