#### 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.

Done