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Order of Tangency Between Manifolds

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Schubert Calculus and Its Applications in Combinatorics and Representation Theory (ICTSC 2017)

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Abstract

We study the order of tangency between two manifolds of same dimension and give that notion three quite different geometric interpretations. Related aspects of the order of tangency, e.g., regular separation exponents, are also discussed.

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Notes

  1. 1.

    Some authors prefer to use at this place Taylor polynomials of degree \(k-1\) instead, see for instance [3] and [4].

  2. 2.

    The standard topology language adopted, among many other sources, in [13]

  3. 3.

    However, this terminology is not yet definitely settled, as shown in a recent work [10]. The authors of the latter speak just descriptively about ‘the Łojasiewicz exponent for the regular separation of closed semialgebraic sets’.

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Acknowledgements

We firstly thank the anonymous referee of [14] for the report which was very stimulating for our present studies. Also, we thank Tadeusz Krasiński for informing us about the regular separation exponents of pairs of sets, a notion due to Łojasiewicz. Lastly, we thank anonymous referees of the present work for their meticulous inspection and advice.

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Authors and Affiliations

  1. Faculty of Mathematics and Information Science, Warsaw University of Technology, Koszykowa 75, 00-662, Warszawa, Poland

    Wojciech Domitrz

  2. Institute of Mathematics, University of Warsaw, Banacha 2, 02-097, Warszawa, Poland

    Piotr Mormul

  3. Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-656, Warszawa, Poland

    Piotr Pragacz

Authors
  1. Wojciech Domitrz
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  2. Piotr Mormul
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  3. Piotr Pragacz
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Corresponding author

Correspondence to Piotr Mormul .

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Editors and Affiliations

  1. School of Mathematics, Sun Yat-sen University, Guangzhou, Guangdong, China

    Jianxun Hu

  2. School of Mathematics, Sun Yat-sen University, Guangzhou, Guangdong, China

    Changzheng Li

  3. Department of Mathematics, Virginia Tech, Blacksburg, VA, USA

    Leonardo C. Mihalcea

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Domitrz, W., Mormul, P., Pragacz, P. (2020). Order of Tangency Between Manifolds. In: Hu, J., Li, C., Mihalcea, L.C. (eds) Schubert Calculus and Its Applications in Combinatorics and Representation Theory. ICTSC 2017. Springer Proceedings in Mathematics & Statistics, vol 332. Springer, Singapore. https://doi.org/10.1007/978-981-15-7451-1_3

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