***This is a course guideline. Students should contact instructor for the updated information on current course syllabus, textbooks, and course content*** Prerequisites: MATH 2415 and six additional ...

Abstract In this paper, we survey some recent results on actions of finite groups on topological manifolds. Given an action of a finite group G on a manifold X, these results provide information on ...

We initiate the study of exotic Dehn twists along 3-manifolds \neq S^3 =S3 inside 4 4-manifolds, which produces the first known examples of exotic diffeomorphisms of contractible 4-manifolds, more ...

We provide an approach to study exotic phenomena in relatively small 4-manifolds that captures many different exotic behaviors under one umbrella. These phenomena include exotic smooth structures on 4 ...

Proceedings of the American Mathematical Society, Vol. 135, No. 6 (Jun., 2007), pp. 1923-1927 (5 pages) Let M be a complete noncompact n-manifold with collapsing volume and Ric ≥ 0. The paper proves ...

A geodesic in a Riemannian homogeneous manifold (M = G/K, g) is called a homogeneous geodesic if it is an orbit of a one-parameter subgroup of the Lie group G. We investigate G-invariant metrics with ...

ABSTRACT: The object of the present paper is to introduce the notion of generalized φ-recurrent Sasakian manifold and study its various geometric properties with the existence of such notion. Among ...