TY - JOUR
T1 - Link homology and equivariant gauge theory
AU - Poudel, Prayat
AU - Saveliev, Nikolai
N1 - Funding Information:
Acknowledgements We are thankful to Ken Baker, Paul Kirk, and Daniel Ruberman for useful discussions. Both authors were partially supported by NSF Grant 1065905.
PY - 2017/9/19
Y1 - 2017/9/19
N2 - Singular instanton Floer homology was defined by Kronheimer and Mrowka in connection with their proof that Khovanov homology is an unknot detector. We study this theory for knots and two-component links using equivariant gauge theory on their double branched covers. We show that the special generator in the singular instanton Floer homology of a knot is graded by the knot signature mod 4, thereby providing a purely topological way of fixing the absolute grading in the theory. Our approach also results in explicit computations of the generators and gradings of the singular instanton Floer chain complex for several classes of knots with simple double branched covers, such as two-bridge knots, some torus knots, and Montesinos knots, as well as for several families of two-component links.
AB - Singular instanton Floer homology was defined by Kronheimer and Mrowka in connection with their proof that Khovanov homology is an unknot detector. We study this theory for knots and two-component links using equivariant gauge theory on their double branched covers. We show that the special generator in the singular instanton Floer homology of a knot is graded by the knot signature mod 4, thereby providing a purely topological way of fixing the absolute grading in the theory. Our approach also results in explicit computations of the generators and gradings of the singular instanton Floer chain complex for several classes of knots with simple double branched covers, such as two-bridge knots, some torus knots, and Montesinos knots, as well as for several families of two-component links.
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U2 - 10.2140/agt.2017.17.2635
DO - 10.2140/agt.2017.17.2635
M3 - Article
AN - SCOPUS:85030669444
VL - 17
SP - 2635
EP - 2685
JO - Algebraic and Geometric Topology
JF - Algebraic and Geometric Topology
SN - 1472-2747
IS - 5
ER -