Room 318

Lusternik-Schnirelmann category of general spaces

Tulsi Srinivasan

Ben Gurion University, Israel.

The Lusternik-Schnirelmann category (LS-category) is a topological invariant
that has historically been studied for absolute neighbourhood retracts. I
will discuss how the theory of the LS-category can be extended to general
metric spaces. Using dimension-theoretic techniques, one can obtain upper
bounds for the LS-category of general spaces by generalising the
Grossman-Whitehead theorem and Dranishnikov's theorem. One can also obtain
lower bounds in terms of cup-length, category weight and Bockstein maps.
These results can be used to calculate the LS-category of some compacta like
the Menger spaces and Pontryagin surfaces. I will also talk about potential
applications of this work to geometric group theory, specifically the
possibility of obtaining an analogue to the Bestvina-Mess formula in terms
of LS-category.