P. Kirk

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math.GT2026

A differential topology proof that the $S U (2)$ character variety of the genus two surface is homeomorphic to $C P^{3}$

Christopher M. Herald, Paul Kirk

We provide a proof that the $S U (2)$ character variety of a genus two surface, $I ¨ (F_{2})$ , is a closed compact manifold, and a proof of the Narasimhan-Ramanan theorem that $I ¨ (F_{2})$ …

math.GT2024

An endomorphism on immersed curves in the pillowcase

Christopher M. Herald, Paul Kirk

We examine the holonomy-perturbed traceless SU(2) character variety of the trivial four-stranded tangle {p_1,p_2,p_3,p_4} X [0,1] in S^2 X [0,1] equipped with a strong marking, eit…

A differential topology proof that the SU(2) character variety of the genus two surface is homeomorphic to CP3

An endomorphism on immersed curves in the pillowcase

A differential topology proof that the $S U (2)$ character variety of the genus two surface is homeomorphic to $C P^{3}$