Article Dans Une Revue Mathematics Année : 2024

Topological Interactions Between Homotopy and Dehn Twist Varieties

Susmit Bagchi
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Résumé

The topological Dehn twists have several applications in mathematical sciences as well as in physical sciences. The interplay between homotopy theory and Dehn twists exposes a rich set of properties. This paper generalizes the Dehn twists by proposing the notion of pre-twisted space, orientations of twists and the formation of pointed based space under a homeomorphic continuous function. It is shown that the Dehn twisted homotopy under non-retraction admits a left lifting property (LLP) through the local homeomorphism. The LLP extends the principles of Hurewicz fibration by avoiding pullback. Moreover, this paper illustrates that the Dehn twisted homotopy up to a base point in a based space can be formed by considering retraction. As a result, two disjoint continuous functions become point-wise continuous at the base point under retracted homotopy twists. Interestingly, the oriented Dehn twists of a pre-twisted space under homotopy retraction mutually commute in a contractible space.

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hal-04759603 , version 1 (30-10-2024)

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Susmit Bagchi. Topological Interactions Between Homotopy and Dehn Twist Varieties. Mathematics , 2024, 12 (20), pp.3282. ⟨10.3390/math12203282⟩. ⟨hal-04759603⟩
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