ar X iv : m at h / 98 10 01 2 v 1 [ m at h . A T ] 2 O ct 1 99 8 . SPACES OF RATIONAL LOOPS ON A REAL PROJECTIVE SPACE

ar X iv : m at h / 04 10 61 1 v 1 [ m at h . A G ] 2 8 O ct 2 00 4 ON RATIONAL CUSPIDAL PROJECTIVE PLANE CURVES

ar X iv : h ep - t h / 01 10 07 9 v 1 9 O ct 2 00 1 Higher Derivative Gravity and Torsion from the Geometry of C - spaces

The geometry of curved Clifford space (C-space) is investigated. It is shown that the curvature in C-space contains higher orders of the curvature in the underlying ordinary space. A C-space is parametrized not only by 1-vector coordinates x µ but also by the 2-vector coordinates σ since they describe the holographic projections of 1-lines, 2-loops, 3-loops, etc., onto the coordinate planes. It...

ar X iv : 0 90 8 . 05 25 v 1 [ m at h . A T ] 4 A ug 2 00 9 PROJECTIVE PRODUCT SPACES DONALD

Let n = (n1, . . . , nr). The quotient space Pn := S n1× · · ·×Snr/(x ∼ −x) is what we call a projective product space. We determine the integral cohomology ring H∗(Pn) and the action of the Steenrod algebra on H∗(Pn;Z2). We give a splitting of ΣPn in terms of stunted real projective spaces, and determine the ring K∗(Pn). We relate the immersion dimension and span of Pn to the much-studied sect...

ar X iv : m at h / 98 07 05 3 v 1 [ m at h . A T ] 1 1 Ju l 1 99 8 SPACES OF POLYNOMIALS WITH ROOTS OF BOUNDED MULTIPLICITY

We describe an alternative approach to some results of Vassiliev ([Va1]) on spaces of polynomials, by using the “scanning method” which was used by Segal ([Se2]) in his investigation of spaces of rational functions. We explain how these two approaches are related by the Smale-Hirsch Principle or the h-Principle of Gromov. We obtain several generalizations, which may be of interest in their own ...

ar X iv : m at h / 98 10 17 2 v 1 [ m at h . D G ] 2 9 O ct 1 99 8 VOLUME OF RIEMANNIAN MANIFOLDS , GEOMETRIC INEQUALITIES , AND HOMOTOPY THEORY

We outline the current state of knowledge regarding geometric inequalities of systolic type, and prove new results, including systolic freedom in dimension 4.