arXiv subjects

Hanife Varli

Publications and source records attributed to Hanife Varli.

3 recordsLinked to original sources

arXiv2019

Elementary Methods for Persistent Homotopy Groups

We study the foundational properties of persistent homotopy groups and develop elementary computational methods for their analysis. Our main theorems are persistent analogues of the Van Kampen, excision, suspension, and Hurewicz theorems. We prove a persistent excision theorem, derive from it a persistent Freudenthal suspension theorem, and obtain a persistent Hurewicz theorem relating the first nonzero persistent homotopy group of a space to its persistent homology. As an application, we compute sublevelset persistent homotopy groups of alkane energy landscapes and show these invariants capture nontrivial loops and higher-dimensional features that comple- ment the information given by persistent homology.

math.AT↗

arXiv2018

Decomposing Perfect Discrete Morse Functions on Connected Sums of 3-manifolds

In this paper, we show that if a closed, connected, oriented 3-manifold M = M1#M2 admits a perfect discrete Morse function, then one can decompose this function as perfect discrete Morse functions on M_1 and M_2. We also give an explicit construction of a separating sphere on M corresponding to such a decomposition.

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arXiv2015

Perfect Discrete Morse Functions on Connected Sums

We study perfect discrete Morse functions on closed oriented n-dimensional manifolds. We show how to compose such functions on connected sums of closed oriented manifolds and how to decompose on connected sums of closed oriented surfaces.

math.AT↗