36 research outputs found
s-Cobordism classification of -manifolds through the group of homotopy self-equivalences
The aim of this paper is to give an -cobordism classification of
topological -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 -manifolds. Using this braid
together with the modified surgery theory of Kreck, we give an -cobordism
classification for certain -manifolds with fundamental group , such
that cd
Homotopy classification of -complexes relative an order relation
We define an order relation among oriented -complexes. We show that
with respect to this relation, two -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