**Date & Time:** Tuesday, September 09, 2014, 16:00-17:00.

**Venue:** Ramanujan Hall

**Title:** Twisted Homology - With Applications to Ring Spectra

**Speaker:** Samik Basu, RKM Vivekananda University

**Abstract:** For a generalised cohomology theory (which has a commutative graded
ring structure) $ R $, one considers the functor which takes a space to the
units in the $0^{th} $ graded piece. This functor can be written as homotopy
classes of maps to some topological space, which we write as $ GL_1R $, and
thus, the action of units on the cohomology ring equips $ R $ with a topological
$ GL_1R $-action. As a consequence a $ 1 $-cocycle with values in $ GL_1R $
gives us new homology and cohomology theories which we call twisted homology and
cohomology. This definition generalises the Thom spectrum of a spherical
fibration. We explore this construction through examples and calculations.