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Topology of cell complexes and manifolds, classification of manifolds (e.g. smoothing, surgery), low dimensional topology (e.g. knot theory, invariants of 4-manifolds), embedding theory, combinatorial and PL topology, geometric group theory, infinite dimensional topology (e.g. Hilbert cube manifolds, theory of retracts).

8 votes
2 answers
273 views

Is there a simple formula to compute the Casson invariant of an homology $3$-sphere from its...

Let $(S_g,\boldsymbol{\alpha}_1,\boldsymbol{\alpha}_2)$ be a Heegaard diagram of a Heegaard splitting $\Sigma=H_g \cup_{\phi_1\phi_2^{-1}}H_g$ of an integral homology sphere $\Sigma$, i.e. $S_g$ is a …
Filippo Bianchi's user avatar
3 votes
1 answer
156 views

Formula for the Casson invariant in terms of the linking form

The paper 'Trisections, intersection forms and the Torelli group' by Peter Lambert-Cole quotes the following formula for the Casson invariant of a knot $K$ in a homology $3$-sphere in terms of the lin …
Filippo Bianchi's user avatar
4 votes
0 answers
105 views

Presentation of handlebody mapping class group

I know some 'nice' infinite presentations of the mapping class group of a surface, such as Gervais' and Luo's. By 'nice' I mean that generators and relations belong to a small number of families. Is t …
Filippo Bianchi's user avatar