# A higher dimensional foliated Donaldson theory, I

@article{Wang2012AHD, title={A higher dimensional foliated Donaldson theory, I}, author={Shuguang Wang}, journal={arXiv: Differential Geometry}, year={2012} }

We introduce the foliated anti-self dual equation for higher dimensional smooth manifolds with codimension-4 Riemannian foliations. Several fundamental results are established, towards the defining of a Donaldson type invariant for such foliations.

#### 9 Citations

Seiberg-Witten invariants on manifolds with Riemannian foliations of codimension 4

- Mathematics
- 2016

Abstract We define Seiberg–Witten equations on closed manifolds endowed with a Riemannian foliation of codimension 4. When the foliation is taut, we show compactness of the moduli space under some… Expand

Transverse $\mathcal F^T$-entropy and transverse Ricci flow for Riemannian foliations

- Mathematics
- 2021

In this paper, we introduced an entropy functional on Riemannian foliation, inspired by the work of Perelman, which is monotonically along the transverse Ricci flow. We relate their gradient flow,… Expand

Transverse FT -entropy and transverse Ricci flow for Riemannian foliations

- 2021

In this paper, we introduced an entropy functional on Riemannian foliation, inspired by the work of Perelman, which is monotonically along the transverse Ricci flow. We relate their gradient flow,… Expand

Moduli spaces of contact instantons

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Abstract We construct the moduli space of contact instantons, an analogue of Yang–Mills instantons defined for contact metric 5-manifolds and initiate the study of their structure. In the K-contact… Expand

Finite dimensional approximation on manifold with codimension-$4$ foliation

- Mathematics
- 2019

For closed manifolds endowed with a Riemannian foliation of codimension $4$, one can define a transversal Seiberg-Witten map. We show that there is a finite dimensional approximation for such a map.… Expand

Monopole Floer homology for codimension-3 Riemannian foliation

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In this paper, we give a systematic study of Seiberg-Witten theory on closed oriented manifold $M$ with codimension-$3$ oriented Riemannian foliation $F$. Under a certain topological condition, we… Expand

Generalised Chern-Simons Theory and G2-Instantons over Associative Fibrations

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- 2014

Adjusting conventional Chern{Simons theory to G2-manifolds, one describes G2-instantons on bundles over a certain class of 7-dimensional flat tori which fiber non- trivially over T 4 , by a pullback… Expand

Moduli space of self-dual connections in dimension greater than four for abelian Gauge groups

- Physics
- 2018

In 1954, C. Yang and R. Mills created a Gauge Theory for strong interaction of Elementary Particles. More generally, they proved that it is possible to define a Gauge Theory with an arbitrary compact… Expand

Index of transverse Dirac operator and cohomotopy Seiberg-Witten invariant for codimension $4$ Riemannian foliation.

- Mathematics
- 2020

For closed manifolds endowed with a Riemannian foliation of codimension $4$, one can define a transversal Seiberg-Witten map. We show that there is a finite dimensional approximation for such a map.… Expand

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