Sorry to ask a question again as I asked a problem in the morning also.
This time I am facing an issue with Mathjax text. As my navbar is fixed, my texts are going inside the navbar whereas the math expressions are going above the navbar. This is annoying me from today's morning itself.
<link href="https://unpkg.com/tailwindcss@^2/dist/tailwind.min.css" rel="stylesheet"
<div >
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<div > <a href="#" >Sachchidanand Prasad</a>
<button @click="open = !open">
<svg fill="currentColor" viewBox="0 0 20 20" >
<path x-show="!open" fill-rule="evenodd" d="M3 5a1 1 0 011-1h12a1 1 0 110 2H4a1 1 0 01-1-1zM3 10a1 1 0 011-1h12a1 1 0 110 2H4a1 1 0 01-1-1zM9 15a1 1 0 011-1h6a1 1 0 110 2h-6a1 1 0 01-1-1z" clip-rule="evenodd"></path>
<path x-show="open" fill-rule="evenodd" d="M4.293 4.293a1 1 0 011.414 0L10 8.586l4.293-4.293a1 1 0 111.414 1.414L11.414 10l4.293 4.293a1 1 0 01-1.414 1.414L10 11.414l-4.293 4.293a1 1 0 01-1.414-1.414L8.586 10 4.293 5.707a1 1 0 010-1.414z" clip-rule="evenodd"></path>
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<nav : > <a href="index.html">
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</a> <a href="research.html">
Research
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CV
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<section >
<div >
<div >
<h2 >Research</h2>
<div ></div>
</div>
<div >
<div >
<div >
<p > My area of interests include <em>differential geometry</em>, <em>differential topology</em> and <em>algebraic topology</em>. More specifically, I am working on <em >cut locus of a submanifold</em>. For a given Riemannian manifold $M$ and $N\subset M$ the <em >cut locus of $N$</em>, $\mathrm{Cu}(N)$, is the collection of points $q\in M$ such that extension of a distance minimal geodesic joining $N$ to $q$ is no longer minimal. Here by the <em >distance minimal geodesic $\gamma$ joining $N$ to $q$</em> we mean that there exists $p\in N$ such that the length of $\gamma$ from $p$ to $q$ is same as the distance from $N$ to $q$. In my recent <a href="#publications" >paper</a> (joint with Dr Somnath Basu) we have discussed the cut locus of a closed submanifold and described the relation between cut locus, Thom spaces and Morse-Bott functions. </p>
<p > Currently, I am working on the cut locus of a quotient manifold and application to the classifying spaces. </p>
<p > </p>
<h2 id="publications">Publications and Preprints</h2>
<ol >
<li > <em>A connection between cut locus, Thom spaces and Morse-Bott functions</em> (joint with Dr Somnath Basu) <a href="ml-8 https://arxiv.org/abs/2011.02972" target="_blank" >ArXiv link</a>
<div >
<p > <span >Abstract:</span> Associated to every closed, embedded submanifold $N$ in a connected Riemannian manifold $M$, there is the distance function $d_N$ which measures the distance of a point in $M$ from $N$. We analyze the square of this function and show that it is Morse-Bott on the complement of the cut locus $\mathrm{Cu}(N)$ of $N$, provided $M$ is complete. Moreover, the gradient flow lines provide a deformation retraction of $M-\mathrm{Cu}(N)$ to $N$. If $M$ is a closed manifold, then we prove that the Thom space of the normal bundle of $N$ is homeomorphic to $M/\mathrm{N}$. We also discuss several interesting results which are either applications of these or related observations regarding the theory of cut locus. These results include, but are not limited to, a computation of the local homology of singular matrices, a classification of the homotopy type of the cut locus of a homology sphere inside a sphere, a deformation of the indefinite unitary group $U(p,q)$ to $U(p)\times U(q)$ and a geometric deformation of $GL(n,\mathbb{R})$ to $O(n,\mathbb{R})$ which is different from the Gram-Schmidt retraction. </p>
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</li>
</ol>
</div>
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</section>
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<h2 >
Useful Links
</h2>
<ul >
<li> <a href="https://mathscinet.ams.org/mathscinet/" target="_blank">MathSciNet</a> </li>
<li> <a href="https://www.ams.org/open-math-notes" target="_blank">AMS open Math Notes</a> </li>
<li> <a href="https://mtts.org.in/" target="_blank">MTTS</a> </li>
<li> <a href="https://www.atmschools.org/" target="_blank">ATM School</a> </li>
</ul>
</div>
<div >
<h2 >
Useful Links
</h2>
<ul >
<li> <a href="http://www.nbhm.dae.gov.in/" target="_blank">NBHM</a> </li>
<li> <a >About Us</a> </li>
<li> <a >Blogs</a> </li>
<li> <a >Contact Us</a> </li>
</ul>
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Social Networks
</h2>
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<li> <a href="">Facebook</a> </li>
<li> <a href="">Twitter</a> </li>
<li> <a href="">Instagram</a> </li>
<li> <a href="">Github</a> </li>
</ul>
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<p > All rights reserved by @ <a href="index.html">Sachchidanand</a> 2022 </p>
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<script src="https://cdn.jsdelivr.net/gh/alpinejs/[email protected]/dist/alpine.min.js" defer></script>
<script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<script>
MathJax = {
tex: {
inlineMath: [
['$', '$'],
['\\(', '\\)']
],
displayMath: [
['$$', '$$'],
['\\[', '\\]']
]
},
svg: {
fontCache: 'global'
}
};
</script>
We can see in the above image that the math text s over the navbar. I don't know what exactly the problem is. Any help will be appreciated.
CodePudding user response：
Insert the tailwind class z-10 to the navbar container to give the navbar a higher z-Index
<link href="https://unpkg.com/tailwindcss@^2/dist/tailwind.min.css" rel="stylesheet"
<div >
<!-- navbar -->
<div >
<div x-data="{ open: false }" >
<div > <a href="#" >Sachchidanand Prasad</a>
<button @click="open = !open">
<svg fill="currentColor" viewBox="0 0 20 20" >
<path x-show="!open" fill-rule="evenodd" d="M3 5a1 1 0 011-1h12a1 1 0 110 2H4a1 1 0 01-1-1zM3 10a1 1 0 011-1h12a1 1 0 110 2H4a1 1 0 01-1-1zM9 15a1 1 0 011-1h6a1 1 0 110 2h-6a1 1 0 01-1-1z" clip-rule="evenodd"></path>
<path x-show="open" fill-rule="evenodd" d="M4.293 4.293a1 1 0 011.414 0L10 8.586l4.293-4.293a1 1 0 111.414 1.414L11.414 10l4.293 4.293a1 1 0 01-1.414 1.414L10 11.414l-4.293 4.293a1 1 0 01-1.414-1.414L8.586 10 4.293 5.707a1 1 0 010-1.414z" clip-rule="evenodd"></path>
</svg>
</button>
</div>
<nav : > <a href="index.html">
Home
</a> <a href="research.html">
Research
</a> <a href="cv.html">
CV
</a> </nav>
</div>
</div>
<!-- section -->
<section >
<div >
<div >
<h2 >Research</h2>
<div ></div>
</div>
<div >
<div >
<div >
<p > My area of interests include <em>differential geometry</em>, <em>differential topology</em> and <em>algebraic topology</em>. More specifically, I am working on <em >cut locus of a submanifold</em>. For a given Riemannian manifold $M$ and $N\subset M$ the <em >cut locus of $N$</em>, $\mathrm{Cu}(N)$, is the collection of points $q\in M$ such that extension of a distance minimal geodesic joining $N$ to $q$ is no longer minimal. Here by the <em >distance minimal geodesic $\gamma$ joining $N$ to $q$</em> we mean that there exists $p\in N$ such that the length of $\gamma$ from $p$ to $q$ is same as the distance from $N$ to $q$. In my recent <a href="#publications" >paper</a> (joint with Dr Somnath Basu) we have discussed the cut locus of a closed submanifold and described the relation between cut locus, Thom spaces and Morse-Bott functions. </p>
<p > Currently, I am working on the cut locus of a quotient manifold and application to the classifying spaces. </p>
<p > </p>
<h2 id="publications">Publications and Preprints</h2>
<ol >
<li > <em>A connection between cut locus, Thom spaces and Morse-Bott functions</em> (joint with Dr Somnath Basu) <a href="ml-8 https://arxiv.org/abs/2011.02972" target="_blank" >ArXiv link</a>
<div >
<p > <span >Abstract:</span> Associated to every closed, embedded submanifold $N$ in a connected Riemannian manifold $M$, there is the distance function $d_N$ which measures the distance of a point in $M$ from $N$. We analyze the square of this function and show that it is Morse-Bott on the complement of the cut locus $\mathrm{Cu}(N)$ of $N$, provided $M$ is complete. Moreover, the gradient flow lines provide a deformation retraction of $M-\mathrm{Cu}(N)$ to $N$. If $M$ is a closed manifold, then we prove that the Thom space of the normal bundle of $N$ is homeomorphic to $M/\mathrm{N}$. We also discuss several interesting results which are either applications of these or related observations regarding the theory of cut locus. These results include, but are not limited to, a computation of the local homology of singular matrices, a classification of the homotopy type of the cut locus of a homology sphere inside a sphere, a deformation of the indefinite unitary group $U(p,q)$ to $U(p)\times U(q)$ and a geometric deformation of $GL(n,\mathbb{R})$ to $O(n,\mathbb{R})$ which is different from the Gram-Schmidt retraction. </p>
</div>
</li>
</ol>
</div>
</div>
</div>
</div>
</section>
<!-- footer -->
<footer >
<div >
<div >
<div >
<h2 >
Useful Links
</h2>
<ul >
<li> <a href="https://mathscinet.ams.org/mathscinet/" target="_blank">MathSciNet</a> </li>
<li> <a href="https://www.ams.org/open-math-notes" target="_blank">AMS open Math Notes</a> </li>
<li> <a href="https://mtts.org.in/" target="_blank">MTTS</a> </li>
<li> <a href="https://www.atmschools.org/" target="_blank">ATM School</a> </li>
</ul>
</div>
<div >
<h2 >
Useful Links
</h2>
<ul >
<li> <a href="http://www.nbhm.dae.gov.in/" target="_blank">NBHM</a> </li>
<li> <a >About Us</a> </li>
<li> <a >Blogs</a> </li>
<li> <a >Contact Us</a> </li>
</ul>
</div>
<div >
<h2 >
Social Networks
</h2>
<ul >
<li> <a href="">Facebook</a> </li>
<li> <a href="">Twitter</a> </li>
<li> <a href="">Instagram</a> </li>
<li> <a href="">Github</a> </li>
</ul>
</div>
</div>
</div>
<div >
<p > All rights reserved by @ <a href="index.html">Sachchidanand</a> 2022 </p>
</div>
</footer>
</div>
<script src="https://cdn.jsdelivr.net/gh/alpinejs/[email protected]/dist/alpine.min.js" defer></script>
<script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<script>
MathJax = {
tex: {
inlineMath: [
['$', '$'],
['\\(', '\\)']
],
displayMath: [
['$$', '$$'],
['\\[', '\\]']
]
},
svg: {
fontCache: 'global'
}
};
</script>