s-Cobordism classification of 44-manifolds through the group of homotopy self-equivalences

The aim of this paper is to give an $s$-cobordism classification of topological $4$-manifolds in terms of the standard invariants using the group of homotopy self-equivalences. Hambleton and Kreck constructed a braid to study the group of homotopy self-equivalences of $4$-manifolds. Using this braid together with the modified surgery theory of Kreck, we give an $s$-cobordism classification for certain $4$-manifolds with fundamental group $\pi$, such that cd $\pi \leq 2$

Homotopy classification of PD4PD_4-complexes relative an order relation

We define an order relation among oriented $PD_4$-complexes. We show that with respect to this relation, two $PD_4$-complexes over the same complex are homotopy equivalent if and only if there is an isometry between the second homology groups. We also consider minimal objects of this relation.Comment: Monatsh. Math. (2015

Generating the Twist Subgroup by Involutions

For a nonorientable surface, the twist subgroup is an index 2 subgroup of the mapping class group. It is generated by Dehn twists about two-sided simple closed curves. In this paper, we study involution generators of the twist subgroup. We give generating sets of involutions with the smallest number of elements our methods allow.Comment: 24 pages, 19 figure

Persistent Homotopy

In this paper, we study some of the basic properties of persistent homotopy. We show that persistent fundamental group benefits from the Van Kampen theorem and the interleaving distance between total spaces is the maximum of the interleaving distances between subspaces. Moreover, we prove excision and Hurewicz theorems for persistent homotopy groups.Comment: 16 pages, 13 figure

Involution Generators of the Big Mapping Class Group

Let S = S(n) denote the infinite surface with n ends, n \in N, accumulated by genus. For n \geq 6, we show that the mapping class group of S is topologically generated by five involutions. When n \geq 3, it is topologically generated by six involutions.Comment: 14 pages, 9 figures. Comments welcome!. arXiv admin note: text overlap with arXiv:2301.08780 by other author