Heim, Mark T., authorAdams, Henry, advisorPeterson, Chris, advisorNeilson, James, committee member2020-06-222020-06-222020https://hdl.handle.net/10217/208461Let G be a group acting properly and by isometries on a metric space X; it follows that the quotient or orbit space X/G is also a metric space. We study the Vietoris–Rips and Čech complexes of X/G. Whereas (co)homology theories for metric spaces let the scale parameter of a Vietoris–Rips or Čech complex go to zero, and whereas geometric group theory requires the scale parameter to be sufficiently large, we instead consider intermediate scale parameters (neither tending to zero nor to infinity). As a particular case, we study the Vietoris–Rips and Čech thickenings of projective spaces at the first scale parameter where the homotopy type changes.born digitalmasters thesesengCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.group actionprojective spaceCech complexVietoris-Rips complexmetric thickeningText